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<b>let </b><font color="Maroon" title="c1">l1</font>, <font color="Maroon" title="c2">l2</font> be    <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> ;<br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c1">l1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">l2</font> &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c1">l1</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="c2">l2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">m1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E3:13"/><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">l1</font> &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c1">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c3">m1</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" title="SCMPDS_2:def.19">SCMPDS_2:def 19</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">m2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E5:13"/><i><font color="Green" title="E12">A3</font></i>: 
( <font color="Maroon" title="c4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l2</font> &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <font color="Maroon" title="c2">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c4">m2</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" title="SCMPDS_2:def.19">SCMPDS_2:def 19</a></i>;<br/>
<a NAME="E6:13"/>
(  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>;<br/>
<b>hence </b><a NAME="E7:13"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_9.html#E1:13"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="scmpds_9.html#E3:13"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E5:13"><i><font color="Green" title="E12">A3</font></i></a></i>;<br/>


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