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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">n</font> be    <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">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c4">a</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/><b>let </b><font color="Maroon" title="c5">il</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>







<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E19">A1</font></i>: 
(  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Maroon" title="c5">il</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">csk</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font>;<br/>
<b>set </b><font color="Maroon" title="c7">csk1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<i><font color="Green" title="E20">A2</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scm_1.html#E21"><i><font color="Green" title="E10">Lm4</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Maroon" title="c5">il</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scm_1.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
;<br/>
<b>hence </b><a NAME="E3:19"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">il</font> )
 <b>by </b><i><a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><b>hence </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmnorm.html#NK1" title="SCMNORM:NK.1">Next</a> 
<b>by </b><i><a class="txt" href="scm_1.html#E1:19"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:19"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
<br/>.= 
 <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

;<br/><br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E5:19"/>
for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font>
 <b>by </b><i><a class="txt" href="scm_1.html#E2:19"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>;<br/>


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