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<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1"><b>suppose </b></a><a NAME="E1:42_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span> ;<br/><b>assume </b><a NAME="E2:42_1_1"/>
not  <a href="amistd_1.html#K2" target="_self">JUMP</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:42_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">l1</font> = 0, <font color="Maroon">l2</font> = 1 as   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <b>by </b><i/>;<br/><a NAME="E6:42_1_1"/>
(  <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">l1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span>  &amp;  <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">l2</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span>  )
 ;<br/><a NAME="E7:42_1_1"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span>  &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> : verum </span>}</span>  )
 <b>by </b><i>, </i>;<br/><a NAME="E8:42_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">1</span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">2</span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/><a NAME="E9:42_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E10:42_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2"><b>suppose </b></a><a NAME="E1:42_1_2"/><i><font color="Green">E39</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">i</font> = <font color="Maroon">i</font> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> ;<br/><a NAME="E3:42_1_2"/>
<font color="Maroon">i</font> is <a href="ami_1.html#V3">halting</a>
 <b>by </b><i>, </i>;<br/><a NAME="E4:42_1_2"/><b>then </b>
for <font color="Olive">l</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> holds   <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Olive">l</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">l</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:42_1_2"/>
 <a href="amistd_1.html#K2" target="_self">JUMP</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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