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

<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</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="c3">k</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>assume </b><a NAME="E1:22"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">s2</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> )
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c1">s1</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#T93" title="AMI_1:th.93">AMI_1:93</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">l</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">NAT</a> <b> such that </b><br/><a NAME="E4:22"/><i><font color="Green" title="E23">A3</font></i>: 
(  <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">l</font> &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  )
 <b>by </b><i><a class="txt" href="scm_1.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>
<a NAME="E5:22"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">l</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c1">s1</font>
 <b>by </b><i><a class="txt" href="scm_1.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scm_1.html#E4:22"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>


</div>
