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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#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</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">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c2">S</font>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E27">A1</font></i>: 
for <font color="Olive" title="b1">f</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font> holds   <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">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Olive" title="b1">f</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E3:39"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="ref" href="yellow_8.html#D1" title="YELLOW_8:def.1">YELLOW_8:def 1</a></i>;<br/>
<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#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">f</font></span>)</span> where <font color="Olive" title="b1">f</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font> : verum </span>}</span> ;<br/>
<b>assume </b><a NAME="E4:39"/>
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/>

<a NAME="E5:39"/><b>then </b>
not  <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">f</font></span>)</span> where <font color="Olive" title="b1">f</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font> : verum </span>}</span>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
;<br/>
<b>then consider </b><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:39"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c7">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">f</font></span>)</span> where <font color="Olive" title="b1">f</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</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="E8:39"/>
(  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></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="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span> )
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:39"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/>
<a NAME="E9:39"/><b>then </b>
( <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</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">f</font></span>)</span> where <font color="Olive" title="b1">f</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font> : verum </span>}</span>  &amp; <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</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">f</font></span>)</span> where <font color="Olive" title="b1">f</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font> : verum </span>}</span>  )
 
;<br/>
<a NAME="E10:39"/><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="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span> )
 
<b>by </b><i><a class="txt" href="amistd_2.html#E7:39"><i><font color="Green" title="E29">A3</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="E11:39"/><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#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <font color="Maroon" title="c5">q</font> )
 
<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="E12:39"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:39"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="amistd_1.html#T36" title="AMISTD_1:th.36">AMISTD_1:36</a></i>;<br/>


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