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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">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">f</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> holds   <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Olive">f</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">p</font> being    <a href="subset_1.html#M2">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>, <font color="Maroon">q</font> being    <a href="subset_1.html#M2">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:39"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="yellow_8.html#D1">YELLOW_8:def 1</a></i>;<br/>
<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">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font></span>)</span> where <font color="Olive">f</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> : verum </span>}</span> ;<br/>
<b>assume </b><a NAME="E4:39"/>
not  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<a NAME="E5:39"/><b>then </b>
not  <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">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font></span>)</span> where <font color="Olive">f</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> : verum </span>}</span>  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="E7:39"/><i><font color="Green">E56</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">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font></span>)</span> where <font color="Olive">f</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E8:39"/>
(  <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">I</font>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">p</font></span>)</span></span><a href="realset1.html#K5">}</a></span> &amp;  <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">I</font>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">q</font></span>)</span></span><a href="realset1.html#K5">}</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E9:39"/><b>then </b>
( <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">p</font></span>)</span></span><a href="realset1.html#K5">}</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">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font></span>)</span> where <font color="Olive">f</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> : verum </span>}</span>  &amp; <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">q</font></span>)</span></span><a href="realset1.html#K5">}</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">NIC</a> <font color="Maroon">I</font>,<font color="Olive">f</font></span>)</span> where <font color="Olive">f</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> : verum </span>}</span>  )
 
;<br/>
<a NAME="E10:39"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">p</font></span>)</span></span><a href="realset1.html#K5">}</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">q</font></span>)</span></span><a href="realset1.html#K5">}</a></span> )
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E11:39"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">p</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K9">NextLoc</a> <font color="Maroon">q</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:39"/>
contradiction
 <b>by </b><i>, <a class="ref" href="amistd_1.html#T36">AMISTD_1:36</a></i>;<br/>


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