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<b>let </b><font color="Maroon" title="c2">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="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_1"/>
(  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span><b>by </b><i><a class="ref" href="amistd_1.html#T22" target="_self" title="AMISTD_1:th.22">Th22</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1"><b>suppose </b></a><a NAME="E1:37_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c4">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span> ;<br/><b>assume </b><a NAME="E2:37_1_1"/>
not  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c3">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:37_1_1"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E5:37_1_1"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ;<br/><a NAME="E6:37_1_1"/><b>then </b>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span> )
 <b>by </b><i><a class="ref" href="amistd_1.html#D11" target="_self" title="AMISTD_1:def.11">Def11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">l1</font> = 0, <font color="Maroon" title="c7">l2</font> = 1 as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E8:37_1_1"/>
(  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c6">l1</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#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span>  &amp;  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c7">l2</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#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span>  )
 ;<br/><a NAME="E9:37_1_1"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <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#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span>  &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <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#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> : verum </span>}</span>  )
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:37_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="amistd_1.html#E39"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/><a NAME="E10:37_1_1"/><b>then </b>
( <font color="Maroon" title="c5">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">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c5">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">2</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="txt" href="amistd_1.html#E4:37_1_1"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/><a NAME="E11:37_1_1"/><b>then </b>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E12:37_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_2"><b>suppose </b></a><a NAME="E1:37_1_2"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c4">i</font> = <font color="Maroon" title="c3">i</font> as   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font></span>)</span> ;<br/><a NAME="E3:37_1_2"/>
<font color="Maroon" title="c4">i</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:37_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="amistd_1.html#T20" target="_self" title="AMISTD_1:th.20">Th20</a></i>;<br/><a NAME="E4:37_1_2"/><b>then </b>
for <font color="Olive" title="b1">l</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c2">N</font> holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">l</font></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#T15" target="_self" title="AMISTD_1:th.15">Th15</a></i>;<br/><b>hence </b><a NAME="E5:37_1_2"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c3">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="amistd_1.html#T14" target="_self" title="AMISTD_1:th.14">Th14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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