<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">i1</font>, <font color="Maroon" title="c3">i2</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E7">A1</font></i>: 
( <font color="Maroon" title="c2">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">i2</font> &amp;  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c3">i2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">m1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E3:9"/><i><font color="Green" title="E8">A2</font></i>: 
( <font color="Maroon" title="c4">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i1</font> &amp;  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c4">m1</font> )
 <b>by </b><i><a class="ref" href="scmring2.html#D10" title="SCMRING2:def.10">SCMRING2:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">m2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E5:9"/><i><font color="Green" title="E9">A3</font></i>: 
( <font color="Maroon" title="c5">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> &amp;  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c3">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c5">m2</font> )
 <b>by </b><i><a class="ref" href="scmring2.html#D10" title="SCMRING2:def.10">SCMRING2:def 10</a></i>;<br/>
<a NAME="E6:9"/>
(  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c4">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 &amp;  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c5">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 )
 
<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="E7:9"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring3.html#E1:9"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="scmring3.html#E3:9"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="scmring3.html#E5:9"><i><font color="Green" title="E9">A3</font></i></a></i>;<br/>


</div>
