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<b>let </b><font color="Maroon" title="c1">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E13">A1</font></i>: 
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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c1">i</font>,<font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Olive" title="b1">l</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E3:16"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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>reconsider </b><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">q</font> = <font color="Maroon" title="c3">q</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</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="c1">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#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span> ;<br/>
<b>assume </b><a NAME="E5:16"/>
not  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">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="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:16"/><i><font color="Green" title="E15">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="c1">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#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : 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="E8:16"/>
(  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="scmpds_9.html#E1:16"><i><font color="Green" title="E13">A1</font></i></a></i>;<br/>
<a NAME="E9:16"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="c1">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#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span>  &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="c1">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#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span>  )
 
;<br/>
<a NAME="E10:16"/><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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c4">p</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="scmpds_9.html#E7:16"><i><font color="Green" title="E15">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="E11:16"/><b>then </b>
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</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="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</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="E12:16"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_9.html#E3:16"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="scmpds_9.html#T10" target="_self" title="SCMPDS_9:th.10">Th10</a></i>;<br/>


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