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<span class="kw">let </span><font color="Maroon" title="c1">s1</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</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>   st  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Olive" title="b1">k</font> holds <br/> <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Olive" title="b1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font> implies  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">s2</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font>;<br/>
<span class="kw">assume </span><a NAME="E1:35"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font></span><br/>

<a NAME="E2:35"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E4:35"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
(  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c4">l</font> &amp;  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">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> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></span>;<br/>
<a NAME="E5:35"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c1">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="ami_1.html#T93" title="AMI_1:th.93">AMI_1:93</a></span>;<br/>
<a NAME="E6:35"/><span class="lab"><font color="Green" title="E26">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<a NAME="E7:35"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">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">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">l</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:35"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<font color="Maroon" title="c1">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E6:35"><span class="lab"><font color="Green" title="E26">T</font></span></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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