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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">steady-programmed</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1"/>
<font color="Maroon" title="c3">s</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">k</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="E3:59_1"/><i><font color="Green" title="E46">A1</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">k</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> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/><b>take </b><font color="Maroon" title="c5">k</font> = <font color="Maroon" title="c4">k</font>;<br/><a NAME="E4:59_1"/>
<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_1.html#K6" title="AMI_1:func.6">IC</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="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c5">k</font></span>)</span></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> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a>, <a class="txt" href="ami_3.html#E3:59_1"><i><font color="Green" title="E46">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:59_1"/>
<font color="Maroon" title="c3">s</font> <a href="ami_3.html#R2" title="AMI_3:pred.2">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c5">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#D15" target="_self" title="AMI_3:def.15">Def15</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c4">k</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><a NAME="E2:59"/><i><font color="Green" title="E46">A2</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="ami_3.html#R2" title="AMI_3:pred.2">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 ;<br/>

<b>take </b>
<font color="Maroon" title="c4">k</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a><br/>

<b>thus </b> <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">k</font></span>)</span> = 
<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_1.html#K6" title="AMI_1:func.6">IC</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="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
<b>by </b><i><a class="txt" href="ami_3.html#E2:59"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="ami_3.html#D15" target="_self" title="AMI_3:def.15">Def15</a></i>
;<br/>


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