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<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">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="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c2">s2</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="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">s2</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a> )
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c1">s1</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="ref" href="scm_1.html#T27" target="_self" title="SCM_1:th.27">Th27</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="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:27"/><i><font color="Green" title="E28">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> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <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#E1:27"><i><font color="Green" title="E26">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="E5:27"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">l</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="c1">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="E6:27"/>
 <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#E1:27"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:27"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="scm_1.html#E4:27"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>


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