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<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">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</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>given </b><font color="Maroon" title="c3">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</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><b> such that </b><a NAME="E1:30"/><i><font color="Green" title="E23">A1</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:30"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c2">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">t</font> = <font color="Maroon" title="c3">s</font> as   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>;<br/>
<a NAME="E4:30"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="ref" href="scmring2.html#T10" target="_self" title="SCMRING2:th.10">Th10</a></i>;<br/>
<a NAME="E5:30"/><i><font color="Green" title="E26">A4</font></i>: 
 <a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
 
<b>by </b><i><a class="ref" href="scmring1.html#D4" title="SCMRING1:def.4">SCMRING1:def 4</a></i>;<br/>
<i><font color="Green" title="E27">A5</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font>
<b>by </b><i><a class="txt" href="scmring2.html#E2:30"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="txt" href="scmring2.html#E4:30"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="scmring1.html#D4" title="SCMRING1:def.4">SCMRING1:def 4</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c5">w</font> = <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 as   <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> <b>by </b><i><a class="txt" href="scmring2.html#E5:30"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">mj</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="E9:30"/><i><font color="Green" title="E28">A6</font></i>: 
( <font color="Maroon" title="c6">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w</font> &amp;  <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c5">w</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="c6">mj</font> )
 <b>by </b><i><a class="ref" href="scmring2.html#D10" target="_self" title="SCMRING2:def.10">Def10</a></i>;<br/>
<a NAME="E10:30"/><i><font color="Green" title="E29">A7</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <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="c5">w</font>
 
<b>by </b><i><a class="txt" href="scmring2.html#E1:30"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="scmring2.html#E4:30"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="scmring1.html#D4" title="SCMRING1:def.4">SCMRING1:def 4</a></i>;<br/>
<a NAME="E11:30"/>
 <a href="scmring2.html#K11" title="SCMRING2:func.11">Next</a> <font color="Maroon" title="c5">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">mj</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="txt" href="scmring2.html#E9:30"><i><font color="Green" title="E28">A6</font></i></a>, <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="E12:30"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring2.html#E6:30"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="scmring2.html#E9:30"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="scmring2.html#E10:30"><i><font color="Green" title="E29">A7</font></i></a></i>;<br/>


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