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

<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V4">halting</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V7">steady-programmed</a> <a href="ami_1.html#V8">definite</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1"/>
<font color="Maroon">s</font> is <a href="ami_1.html#V9">halting</a>
 ;<br/><b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:59_1"/><i><font color="Green">E24</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/><b>take </b><font color="Maroon">k</font> = <font color="Maroon">k</font>;<br/><a NAME="E4:59_1"/>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a>, <a class="ref" href="ami_3.html#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E5:59_1"/>
<font color="Maroon">s</font> <a href="ami_3.html#R2" target="_self">halts_at</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#D11" target="_self">Def11</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><a NAME="E2:59"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">s</font> <a href="ami_3.html#R2" target="_self">halts_at</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 ;<br/>

<b>take </b>
<font color="Maroon">k</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a><br/>

<b>thus </b> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> = 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
<b>by </b><i><a class="ref" href="ami_3.html#T8" target="_self">Th8</a>, <a class="ref" href="ami_3.html#D11" target="_self">Def11</a></i>
;<br/>


</div>
