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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V6" title="AMI_1:attr.6">steady-programmed</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">without_implicit_jumps</a> <a href="amistd_2.html#V8" title="AMISTD_2:attr.8">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font>, <font color="Maroon" title="c5">H</font> be   <a href="amistd_1.html#NM1" title="AMISTD_1:NM.1">pre-Macro</a> of <font color="Maroon" title="c2">S</font>;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:135_1"/>
( <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font> or <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font> or ( <font color="Maroon" title="c3">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c4">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1"><b>suppose </b></a><a NAME="E1:135_1_1"/><i><font color="Green" title="E70">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font> = 
<font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T60" target="_self" title="AMISTD_2:th.60">Th60</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="ref" href="amistd_2.html#T60" target="_self" title="AMISTD_2:th.60">Th60</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_2"><b>suppose </b></a><a NAME="E1:135_1_2"/><i><font color="Green" title="E70">A2</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font> = 
<font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T59" target="_self" title="AMISTD_2:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_2"><i><font color="Green" title="E70">A2</font></i></a>, <a class="ref" href="amistd_2.html#T60" target="_self" title="AMISTD_2:th.60">Th60</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:135_1_3"/><i><font color="Green" title="E70">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font>
 <b>and </b><br/><a NAME="E2:135_1_3"/><i><font color="Green" title="E71">A4</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c6">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 </span>}</span> ;<br/><i><font color="Green" title="E72">A5</font></i>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

;<br/><i><font color="Green" title="E73">A6</font></i>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

;<br/><a NAME="E5:135_1_3"/><i><font color="Green" title="E74">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3"><i><font color="Green" title="E72">A5</font></i></a>, <a class="ref" href="amistd_2.html#T15" target="_self" title="AMISTD_2:th.15">Th15</a></i>;<br/><a NAME="E6:135_1_3"/><i><font color="Green" title="E75">A8</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3"><i><font color="Green" title="E73">A6</font></i></a>, <a class="ref" href="amistd_2.html#T15" target="_self" title="AMISTD_2:th.15">Th15</a></i>;<br/><a NAME="E7:135_1_3"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b2">k</font></span>)</span> where <font color="Olive" title="b2">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 </span>}</span>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:135_1_3_3"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3"/><i><font color="Green" title="E76">A9</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c8">k</font>
 <b>and </b><br/><a NAME="E4:135_1_3_3"/><i><font color="Green" title="E77">A10</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 ;<br/>
<a NAME="E5:135_1_3_3"/><i><font color="Green" title="E78">A11</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<a NAME="E6:135_1_3_3"/><i><font color="Green" title="E79">A12</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<a NAME="E7:135_1_3_3"/><i><font color="Green" title="E80">A13</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<i><font color="Green" title="E81">A14</font></i>: <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>
;<br/>
<a NAME="E9:135_1_3_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 
;<br/>
<b>then </b><i><font color="Green" title="E82">A15</font></i>: <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
;<br/>
<a NAME="E11:135_1_3_3"/><i><font color="Green" title="E83">A16</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<a NAME="E12:135_1_3_3"/><i><font color="Green" title="E84">A17</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/>
<a NAME="E13:135_1_3_3"/><i><font color="Green" title="E85">A18</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/>
<a NAME="E14:135_1_3_3"/><i><font color="Green" title="E86">A19</font></i>: 
for <font color="Olive" title="b1">W</font> being  <a href="amistd_1.html#NM1" title="AMISTD_1:NM.1">pre-Macro</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font> holds <br/>2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">W</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">W</font> be   <a href="amistd_1.html#NM1" title="AMISTD_1:NM.1">pre-Macro</a> of <font color="Maroon" title="c2">S</font>;<br/>

<b>assume </b><a NAME="E1:135_1_3_3_3"/>
<font color="Maroon" title="c9">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">Stop</a> <font color="Maroon" title="c2">S</font>
 ;<br/>

<a NAME="E2:135_1_3_3_3"/><b>then </b><i><font color="Green" title="E87">A20</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="amistd_2.html#T26" target="_self" title="AMISTD_2:th.26">Th26</a></i>;<br/>
<a NAME="E3:135_1_3_3_3"/><i><font color="Green" title="E88">A21</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<b>assume </b><a NAME="E4:135_1_3_3_3"/>
2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">W</font>
 ;<br/>

<a NAME="E5:135_1_3_3_3"/><b>then </b>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">W</font>
 
;<br/>
<a NAME="E6:135_1_3_3_3"/><b>then </b>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">W</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:135_1_3_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_3"><i><font color="Green" title="E87">A20</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_3"><i><font color="Green" title="E88">A21</font></i></a>, <a class="ref" href="nat_1.html#T26" title="NAT_1:th.26">NAT_1:26</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E15:135_1_3_3"/><b>then </b>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3"><i><font color="Green" title="E70">A3</font></i></a></i>;<br/>
<a NAME="E16:135_1_3_3"/><b>then </b><i><font color="Green" title="E87">A22</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E17:135_1_3_3"/><i><font color="Green" title="E88">A23</font></i>: 
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3"><i><font color="Green" title="E71">A4</font></i></a>, <a class="txt" href="amistd_2.html#E14:135_1_3_3"><i><font color="Green" title="E86">A19</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_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="E1:135_1_3_3_4"/>
( <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 or <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 or (  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3 ) or <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font> )
 </span><b>by </b><i><a class="txt" href="amistd_2.html#E16:135_1_3_3"><i><font color="Green" title="E87">A22</font></i></a>, <a class="txt" href="amistd_2.html#E17:135_1_3_3"><i><font color="Green" title="E88">A23</font></i></a>, <a class="txt" href="amistd_2.html#E14"><i><font color="Green" title="E8">Lm2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3_3_4_1"><b>suppose </b></a><a NAME="E1:135_1_3_3_4_1"/><i><font color="Green" title="E89">A24</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 ;<br/><div class="add"><a NAME="E2:135_1_3_3_4_1"/><i><font color="Green" title="E90">A25</font></i>: 
 <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T54" target="_self" title="AMISTD_2:th.54">Th54</a></i>;<br/><div><i><font color="Green" title="E91">A26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_1_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3_4_1_1"/><i><font color="Green" title="E92">A27</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:135_1_3_3_4_1_1"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3"><i><font color="Green" title="E78">A11</font></i></a></i>;<br/><font color="Maroon" title="c8">k</font> = 
<font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_1_1"><i><font color="Green" title="E92">A27</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>
<br/>.= 
<font color="Maroon" title="c9">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
;<br/><a NAME="E6:135_1_3_3_4_1_1"/><b>then </b>
<font color="Maroon" title="c9">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_1"><i><font color="Green" title="E89">A24</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E7:135_1_3_3_4_1_1"/><b>then </b>
<font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><b>hence </b><a NAME="E8:135_1_3_3_4_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green" title="E92">A28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_1_2"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3_4_1_2"/><i><font color="Green" title="E93">A29</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:135_1_3_3_4_1_2"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3"><i><font color="Green" title="E79">A12</font></i></a></i>;<br/><a NAME="E5:135_1_3_3_4_1_2"/>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_1_2"><i><font color="Green" title="E93">A29</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><a NAME="E6:135_1_3_3_4_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_1"><i><font color="Green" title="E89">A24</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><b>hence </b><a NAME="E7:135_1_3_3_4_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/></div><b>end;</b></div><a NAME="E5:135_1_3_3_4_1"/>
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_1"><i><font color="Green" title="E89">A24</font></i></a>, <a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/><a NAME="E6:135_1_3_3_4_1"/><b>then </b><i><font color="Green" title="E93">A30</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3_3_4_1"><i><font color="Green" title="E92">A28</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_1"><i><font color="Green" title="E90">A25</font></i></a>, <a class="txt" href="amistd_2.html#E6:135_1_3_3_4_1"><i><font color="Green" title="E93">A30</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3_4_1"><i><font color="Green" title="E91">A26</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3_3_4_2"><b>suppose </b></a><a NAME="E1:135_1_3_3_4_2"/><i><font color="Green" title="E89">A31</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 ;<br/><div class="add"><div><i><font color="Green" title="E90">A32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_2_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3_4_2_1"/><i><font color="Green" title="E91">A33</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:135_1_3_3_4_2_1"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3"><i><font color="Green" title="E79">A12</font></i></a></i>;<br/><a NAME="E5:135_1_3_3_4_2_1"/>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_2_1"><i><font color="Green" title="E91">A33</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><a NAME="E6:135_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_2"><i><font color="Green" title="E89">A31</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E7:135_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="nat_1.html#T7" title="NAT_1:th.7">NAT_1:7</a></i>;<br/><a NAME="E8:135_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><b>hence </b><a NAME="E9:135_1_3_3_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3"><i><font color="Green" title="E71">A4</font></i></a>, <a class="ref" href="amistd_2.html#T26" target="_self" title="AMISTD_2:th.26">Th26</a></i>;<br/></div><b>end;</b></div><a NAME="E3:135_1_3_3_4_2"/><i><font color="Green" title="E91">A34</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E4:135_1_3_3_4_2"/><i><font color="Green" title="E92">A35</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E5:135_1_3_3_4_2"/><i><font color="Green" title="E93">A36</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E6:135_1_3_3_4_2"/><i><font color="Green" title="E94">A37</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E7:135_1_3_3_4_2"/>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_2"><i><font color="Green" title="E89">A31</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E8:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E95">A38</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E5:135_1_3_3"><i><font color="Green" title="E78">A11</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_2"><i><font color="Green" title="E91">A34</font></i></a></i>;<br/><a NAME="E9:135_1_3_3_4_2"/><i><font color="Green" title="E96">A39</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_2"><i><font color="Green" title="E89">A31</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E10:135_1_3_3_4_2"/><i><font color="Green" title="E97">A40</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a></i>;<br/><a NAME="E11:135_1_3_3_4_2"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E12:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E98">A41</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E11:135_1_3_3"><i><font color="Green" title="E83">A16</font></i></a>, <a class="txt" href="amistd_2.html#E9:135_1_3_3_4_2"><i><font color="Green" title="E96">A39</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3_4_2"><i><font color="Green" title="E97">A40</font></i></a></i>;<br/><a NAME="E13:135_1_3_3_4_2"/><b>then </b>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E14:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E99">A42</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_2_2"><b>now </b></a><div class="add"><i><font color="Green" title="E100">A43</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55" title="AMISTD_1:th.55">AMISTD_1:55</a></i>
;<br/><b>assume </b><a NAME="E2:135_1_3_3_4_2_2"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E3:135_1_3_3_4_2_2"/><b>then </b>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_2_2"><i><font color="Green" title="E100">A43</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:135_1_3_3_4_2_2"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><a NAME="E5:135_1_3_3_4_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E9:135_1_3_3_4_2"><i><font color="Green" title="E96">A39</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><b>hence </b><a NAME="E6:135_1_3_3_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3"><i><font color="Green" title="E71">A4</font></i></a>, <a class="ref" href="amistd_2.html#T26" target="_self" title="AMISTD_2:th.26">Th26</a></i>;<br/></div><b>end;</b></div><a NAME="E16:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E100">A44</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14:135_1_3_3_4_2"><i><font color="Green" title="E99">A42</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E17:135_1_3_3_4_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:135_1_3_3_4_2_3"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<b>hence </b><a NAME="E2:135_1_3_3_4_2_3"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font> )
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3"><i><font color="Green" title="E71">A4</font></i></a>, <a class="ref" href="amistd_2.html#T26" target="_self" title="AMISTD_2:th.26">Th26</a>, <a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a><br/>


</div><b>end;</b></div><a NAME="E18:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E101">A45</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E19:135_1_3_3_4_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E20:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E102">A46</font></i>: 
not  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T41" target="_self" title="AMISTD_2:th.41">Th41</a></i>;<br/><a NAME="E21:135_1_3_3_4_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_2"><i><font color="Green" title="E101">A45</font></i></a>, <a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/><a NAME="E22:135_1_3_3_4_2"/><b>then </b><i><font color="Green" title="E103">A47</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a>, <a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a></i>;<br/><i><font color="Green" title="E104">A48</font></i>:  <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3_4_2"><i><font color="Green" title="E93">A36</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E22:135_1_3_3_4_2"><i><font color="Green" title="E103">A47</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E20:135_1_3_3_4_2"><i><font color="Green" title="E102">A46</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_2"><i><font color="Green" title="E94">A37</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_2"><i><font color="Green" title="E90">A32</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E16:135_1_3_3_4_2"><i><font color="Green" title="E100">A44</font></i></a>, <a class="ref" href="grfunc_1.html#T93" title="GRFUNC_1:th.93">GRFUNC_1:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E12:135_1_3_3_4_2"><i><font color="Green" title="E98">A41</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3_3_4_2"><i><font color="Green" title="E92">A35</font></i></a>, <a class="txt" href="amistd_2.html#E9:135_1_3_3_4_2"><i><font color="Green" title="E96">A39</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3_4_2"><i><font color="Green" title="E97">A40</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3_4_2"><i><font color="Green" title="E93">A36</font></i></a>, <a class="txt" href="amistd_2.html#E23:135_1_3_3_4_2"><i><font color="Green" title="E104">A48</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_2"><i><font color="Green" title="E94">A37</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3_4_2"><i><font color="Green" title="E91">A34</font></i></a>, <a class="txt" href="amistd_2.html#E9:135_1_3_3_4_2"><i><font color="Green" title="E96">A39</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3_4_2"><i><font color="Green" title="E97">A40</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3_4_2"><i><font color="Green" title="E95">A38</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3_3_4_3"><b>suppose </b></a><b>that </b><a NAME="E1:135_1_3_3_4_3"/><i><font color="Green" title="E89">A49</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 <b>and </b><br/><a NAME="E2:135_1_3_3_4_3"/><i><font color="Green" title="E90">A50</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3
 ;<br/><div class="add"><div><i><font color="Green" title="E91">A51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_3_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3_4_3_1"/><i><font color="Green" title="E92">A52</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:135_1_3_3_4_3_1"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3"><i><font color="Green" title="E79">A12</font></i></a></i>;<br/><a NAME="E5:135_1_3_3_4_3_1"/>
<font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E12:135_1_3_3"><i><font color="Green" title="E84">A17</font></i></a>, <a class="txt" href="amistd_2.html#E13:135_1_3_3"><i><font color="Green" title="E85">A18</font></i></a>, <a class="txt" href="amistd_2.html#E2:135_1_3_3_4_3"><i><font color="Green" title="E90">A50</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_3_1"><i><font color="Green" title="E92">A52</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><a NAME="E6:135_1_3_3_4_3_1"/><b>then </b>
<font color="Maroon" title="c9">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E7:135_1_3_3_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E13"><i><font color="Green" title="E7">Lm1</font></i></a></i>;<br/></div><b>end;</b></div><a NAME="E4:135_1_3_3_4_3"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E5:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_3"><i><font color="Green" title="E89">A49</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E92">A53</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E7:135_1_3_3_4_3"/><i><font color="Green" title="E93">A54</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:135_1_3_3_4_3"><i><font color="Green" title="E89">A49</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E8:135_1_3_3_4_3"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E9:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3_4_3"><i><font color="Green" title="E93">A54</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E10:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E94">A55</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E11:135_1_3_3_4_3"/><i><font color="Green" title="E95">A56</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E12:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E96">A57</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_3"><i><font color="Green" title="E90">A50</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E13:135_1_3_3_4_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_3"><i><font color="Green" title="E90">A50</font></i></a>, <a class="txt" href="amistd_2.html#E11:135_1_3_3_4_3"><i><font color="Green" title="E95">A56</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E14:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E15:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E16:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3_4_3"><i><font color="Green" title="E94">A55</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E17:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/><a NAME="E18:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E97">A58</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><a NAME="E19:135_1_3_3_4_3"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E20:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E98">A59</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/><a NAME="E21:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E99">A60</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E22:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E100">A61</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3"><i><font color="Green" title="E78">A11</font></i></a>, <a class="txt" href="amistd_2.html#E6:135_1_3_3_4_3"><i><font color="Green" title="E92">A53</font></i></a></i>;<br/><a NAME="E23:135_1_3_3_4_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E24:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E12:135_1_3_3_4_3"><i><font color="Green" title="E96">A57</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E25:135_1_3_3_4_3"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>;<br/><a NAME="E26:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E101">A62</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_3_2"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:135_1_3_3_4_3_2"/><b>then </b>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><b>then </b><font color="Maroon" title="c7">x</font> = 
 <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55" title="AMISTD_1:th.55">AMISTD_1:55</a></i>
;<br/><b>then </b><font color="Maroon" title="c8">k</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
<b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E13:135_1_3_3"><i><font color="Green" title="E85">A18</font></i></a>, <a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
;<br/><b>hence </b><a NAME="E5:135_1_3_3_4_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_3"><i><font color="Green" title="E90">A50</font></i></a>, <a class="txt" href="amistd_2.html#E11:135_1_3_3_4_3"><i><font color="Green" title="E95">A56</font></i></a></i>;<br/></div><b>end;</b></div><a NAME="E28:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E102">A63</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E26:135_1_3_3_4_3"><i><font color="Green" title="E101">A62</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E29:135_1_3_3_4_3"/><i><font color="Green" title="E103">A64</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/><a NAME="E30:135_1_3_3_4_3"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_3"><i><font color="Green" title="E97">A58</font></i></a></i>;<br/><a NAME="E31:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E104">A65</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E32:135_1_3_3_4_3"/><b>then </b><i><font color="Green" title="E105">A66</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E11:135_1_3_3"><i><font color="Green" title="E83">A16</font></i></a>, <a class="txt" href="amistd_2.html#E6:135_1_3_3_4_3"><i><font color="Green" title="E92">A53</font></i></a></i>;<br/><div><i><font color="Green" title="E106">A67</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_3_3_4_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:135_1_3_3_4_3_3"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:135_1_3_3_4_3_3"/><i><font color="Green" title="E107">A68</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:135_1_3_3_4_3_3"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3"><i><font color="Green" title="E80">A13</font></i></a></i>;<br/><a NAME="E5:135_1_3_3_4_3_3"/>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3_4_3_3"><i><font color="Green" title="E107">A68</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><b>then </b><i><font color="Green" title="E108">A69</font></i>: <font color="Maroon" title="c9">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3_4_3"><i><font color="Green" title="E94">A55</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
<br/>.= 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span>

;<br/><a NAME="E7:135_1_3_3_4_3_3"/>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_3"><i><font color="Green" title="E90">A50</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E8:135_1_3_3_4_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_3_3"><i><font color="Green" title="E108">A69</font></i></a>, <a class="txt" href="amistd_2.html#E13"><i><font color="Green" title="E7">Lm1</font></i></a></i>;<br/></div><b>end;</b></div><i><font color="Green" title="E107">A70</font></i>:  <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E20:135_1_3_3_4_3"><i><font color="Green" title="E98">A59</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E33:135_1_3_3_4_3"><i><font color="Green" title="E106">A67</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_3"><i><font color="Green" title="E97">A58</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3_4_3"><i><font color="Green" title="E91">A51</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E28:135_1_3_3_4_3"><i><font color="Green" title="E102">A63</font></i></a>, <a class="ref" href="grfunc_1.html#T93" title="GRFUNC_1:th.93">GRFUNC_1:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E32:135_1_3_3_4_3"><i><font color="Green" title="E105">A66</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_3"><i><font color="Green" title="E92">A53</font></i></a>, <a class="txt" href="amistd_2.html#E31:135_1_3_3_4_3"><i><font color="Green" title="E104">A65</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_3"><i><font color="Green" title="E97">A58</font></i></a>, <a class="txt" href="amistd_2.html#E29:135_1_3_3_4_3"><i><font color="Green" title="E103">A64</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_3"><i><font color="Green" title="E97">A58</font></i></a>, <a class="txt" href="amistd_2.html#E29:135_1_3_3_4_3"><i><font color="Green" title="E103">A64</font></i></a>, <a class="txt" href="amistd_2.html#E34:135_1_3_3_4_3"><i><font color="Green" title="E107">A70</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E20:135_1_3_3_4_3"><i><font color="Green" title="E98">A59</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_3"><i><font color="Green" title="E92">A53</font></i></a>, <a class="txt" href="amistd_2.html#E21:135_1_3_3_4_3"><i><font color="Green" title="E99">A60</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E22:135_1_3_3_4_3"><i><font color="Green" title="E100">A61</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3_3_4_4"><b>suppose </b></a><a NAME="E1:135_1_3_3_4_4"/><i><font color="Green" title="E89">A71</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2
 ;<br/><div class="add"><a NAME="E2:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E90">A72</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E3:135_1_3_3_4_4"/>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_4"><i><font color="Green" title="E89">A71</font></i></a></i>;<br/><a NAME="E4:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E91">A73</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E5:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E92">A74</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E6:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E93">A75</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3"><i><font color="Green" title="E79">A12</font></i></a>, <a class="txt" href="amistd_2.html#E2:135_1_3_3_4_4"><i><font color="Green" title="E90">A72</font></i></a></i>;<br/><a NAME="E7:135_1_3_3_4_4"/><i><font color="Green" title="E94">A76</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E12:135_1_3_3"><i><font color="Green" title="E84">A17</font></i></a>, <a class="txt" href="amistd_2.html#E13:135_1_3_3"><i><font color="Green" title="E85">A18</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_4"><i><font color="Green" title="E89">A71</font></i></a></i>;<br/><a NAME="E8:135_1_3_3_4_4"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/><a NAME="E9:135_1_3_3_4_4"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font>
 ;<br/><a NAME="E10:135_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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E11:135_1_3_3_4_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E12:135_1_3_3_4_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>;<br/><a NAME="E13:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E95">A77</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><a NAME="E14:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E96">A78</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E15:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E97">A79</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3"><i><font color="Green" title="E78">A11</font></i></a>, <a class="txt" href="amistd_2.html#E7:135_1_3_3_4_4"><i><font color="Green" title="E94">A76</font></i></a></i>;<br/><a NAME="E16:135_1_3_3_4_4"/><i><font color="Green" title="E98">A80</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><a NAME="E17:135_1_3_3_4_4"/><i><font color="Green" title="E99">A81</font></i>: 
 <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E13:135_1_3_3_4_4"><i><font color="Green" title="E95">A77</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>;<br/><a NAME="E18:135_1_3_3_4_4"/><i><font color="Green" title="E100">A82</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49" title="AMISTD_1:th.49">AMISTD_1:49</a></i>;<br/><b>then </b><i><font color="Green" title="E101">A83</font></i>:  <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E16:135_1_3_3_4_4"><i><font color="Green" title="E98">A80</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
;<br/> <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E17:135_1_3_3_4_4"><i><font color="Green" title="E99">A81</font></i></a>, <a class="ref" href="amistd_1.html#T55" title="AMISTD_1:th.55">AMISTD_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T55" target="_self" title="AMISTD_2:th.55">Th55</a></i>
<br/>.= 
 <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_4"><i><font color="Green" title="E100">A82</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
;<br/><a NAME="E21:135_1_3_3_4_4"/><b>then </b><i><font color="Green" title="E102">A84</font></i>: 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E19:135_1_3_3_4_4"><i><font color="Green" title="E101">A83</font></i></a>, <a class="ref" href="amistd_2.html#T37" target="_self" title="AMISTD_2:th.37">Th37</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3_4_4"><i><font color="Green" title="E93">A75</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_4"><i><font color="Green" title="E90">A72</font></i></a>, <a class="txt" href="amistd_2.html#E5:135_1_3_3_4_4"><i><font color="Green" title="E92">A74</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3_3_4_4"><i><font color="Green" title="E91">A73</font></i></a>, <a class="txt" href="amistd_2.html#E16:135_1_3_3_4_4"><i><font color="Green" title="E98">A80</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E13:135_1_3_3_4_4"><i><font color="Green" title="E95">A77</font></i></a>, <a class="txt" href="amistd_2.html#E21:135_1_3_3_4_4"><i><font color="Green" title="E102">A84</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3_4_4"><i><font color="Green" title="E94">A76</font></i></a>, <a class="txt" href="amistd_2.html#E14:135_1_3_3_4_4"><i><font color="Green" title="E96">A78</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E15:135_1_3_3_4_4"><i><font color="Green" title="E97">A79</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_3_3_4_5"><b>suppose </b></a><a NAME="E1:135_1_3_3_4_5"/><i><font color="Green" title="E89">A85</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k</font>
 ;<br/><div class="add"><a NAME="E2:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E90">A86</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E3:135_1_3_3_4_5"/><i><font color="Green" title="E91">A87</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_5"><i><font color="Green" title="E89">A85</font></i></a>, <a class="ref" href="xreal_1.html#T50" title="XREAL_1:th.50">XREAL_1:50</a></i>;<br/><a NAME="E4:135_1_3_3_4_5"/>
<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3_3"><i><font color="Green" title="E77">A10</font></i></a></i>;<br/><a NAME="E5:135_1_3_3_4_5"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T23" title="XREAL_1:th.23">XREAL_1:23</a></i>;<br/><a NAME="E6:135_1_3_3_4_5"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E3:135_1_3_3_4_5"><i><font color="Green" title="E91">A87</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E7:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E92">A88</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><a NAME="E8:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E93">A89</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E9:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E94">A90</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:135_1_3_3"><i><font color="Green" title="E79">A12</font></i></a>, <a class="txt" href="amistd_2.html#E2:135_1_3_3_4_5"><i><font color="Green" title="E90">A86</font></i></a></i>;<br/><a NAME="E10:135_1_3_3_4_5"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E11:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E95">A91</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_5"><i><font color="Green" title="E89">A85</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E96">A92</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:135_1_3_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E13:135_1_3_3_4_5"/><i><font color="Green" title="E97">A93</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E11:135_1_3_3_4_5"><i><font color="Green" title="E95">A91</font></i></a>, <a class="ref" href="xreal_1.html#T50" title="XREAL_1:th.50">XREAL_1:50</a></i>;<br/><a NAME="E14:135_1_3_3_4_5"/><i><font color="Green" title="E98">A94</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:135_1_3_3"><i><font color="Green" title="E77">A10</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E15:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E99">A95</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E12:135_1_3_3"><i><font color="Green" title="E84">A17</font></i></a>, <a class="txt" href="amistd_2.html#E13:135_1_3_3_4_5"><i><font color="Green" title="E97">A93</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E16:135_1_3_3_4_5"/>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E12:135_1_3_3"><i><font color="Green" title="E84">A17</font></i></a>, <a class="txt" href="amistd_2.html#E13:135_1_3_3_4_5"><i><font color="Green" title="E97">A93</font></i></a>, <a class="txt" href="amistd_2.html#E14:135_1_3_3_4_5"><i><font color="Green" title="E98">A94</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E17:135_1_3_3_4_5"/><b>then </b>
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>;<br/><a NAME="E18:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E100">A96</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><a NAME="E19:135_1_3_3_4_5"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E20:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E101">A97</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3_3"><i><font color="Green" title="E78">A11</font></i></a>, <a class="txt" href="amistd_2.html#E12:135_1_3_3_4_5"><i><font color="Green" title="E96">A92</font></i></a></i>;<br/><a NAME="E21:135_1_3_3_4_5"/><i><font color="Green" title="E102">A98</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_5"><i><font color="Green" title="E100">A96</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E22:135_1_3_3_4_5"/><i><font color="Green" title="E103">A99</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_5"><i><font color="Green" title="E89">A85</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E23:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E104">A100</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E11:135_1_3_3_4_5"><i><font color="Green" title="E95">A91</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/><a NAME="E24:135_1_3_3_4_5"/><i><font color="Green" title="E105">A101</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E11:135_1_3_3_4_5"><i><font color="Green" title="E95">A91</font></i></a>, <a class="txt" href="amistd_2.html#E22:135_1_3_3_4_5"><i><font color="Green" title="E103">A99</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/><a NAME="E25:135_1_3_3_4_5"/><i><font color="Green" title="E106">A102</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E23:135_1_3_3_4_5"><i><font color="Green" title="E104">A100</font></i></a>, <a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E26:135_1_3_3_4_5"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E13:135_1_3_3"><i><font color="Green" title="E85">A18</font></i></a>, <a class="txt" href="amistd_2.html#E15:135_1_3_3_4_5"><i><font color="Green" title="E99">A95</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E27:135_1_3_3_4_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E24:135_1_3_3_4_5"><i><font color="Green" title="E105">A101</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/><a NAME="E28:135_1_3_3_4_5"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/><a NAME="E29:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E107">A103</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E30:135_1_3_3_4_5"/><b>then </b><i><font color="Green" title="E108">A104</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3"><i><font color="Green" title="E80">A13</font></i></a>, <a class="txt" href="amistd_2.html#E25:135_1_3_3_4_5"><i><font color="Green" title="E106">A102</font></i></a></i>;<br/><i><font color="Green" title="E109">A105</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E23:135_1_3_3_4_5"><i><font color="Green" title="E104">A100</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:135_1_3_3_4_5"><i><font color="Green" title="E95">A91</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon" title="c8">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>

<br/>.= 
<font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E8:135_1_3_3"><i><font color="Green" title="E81">A14</font></i></a>, <a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E1:135_1_3_3_4_5"><i><font color="Green" title="E89">A85</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
;<br/><i><font color="Green" title="E110">A106</font></i>:  <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_5"><i><font color="Green" title="E100">A96</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E30:135_1_3_3_4_5"><i><font color="Green" title="E108">A104</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E25:135_1_3_3_4_5"><i><font color="Green" title="E106">A102</font></i></a>, <a class="txt" href="amistd_2.html#E29:135_1_3_3_4_5"><i><font color="Green" title="E107">A103</font></i></a>, <a class="txt" href="amistd_2.html#E31:135_1_3_3_4_5"><i><font color="Green" title="E109">A105</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3_4_5"><i><font color="Green" title="E92">A88</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E9:135_1_3_3_4_5"><i><font color="Green" title="E94">A90</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:135_1_3_3_4_5"><i><font color="Green" title="E90">A86</font></i></a>, <a class="txt" href="amistd_2.html#E8:135_1_3_3_4_5"><i><font color="Green" title="E93">A89</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c5">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E7:135_1_3_3_4_5"><i><font color="Green" title="E92">A88</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:135_1_3_3"><i><font color="Green" title="E82">A15</font></i></a>, <a class="txt" href="amistd_2.html#E32:135_1_3_3_4_5"><i><font color="Green" title="E110">A106</font></i></a>, <a class="ref" href="amistd_2.html#T37" target="_self" title="AMISTD_2:th.37">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E18:135_1_3_3_4_5"><i><font color="Green" title="E100">A96</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E12:135_1_3_3_4_5"><i><font color="Green" title="E96">A92</font></i></a>, <a class="txt" href="amistd_2.html#E21:135_1_3_3_4_5"><i><font color="Green" title="E102">A98</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E20:135_1_3_3_4_5"><i><font color="Green" title="E101">A97</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">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="E8:135_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="amistd_2.html#K13" title="AMISTD_2:func.13">';'</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:135_1_3"><i><font color="Green" title="E74">A7</font></i></a>, <a class="txt" href="amistd_2.html#E6:135_1_3"><i><font color="Green" title="E75">A8</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
