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<b>let </b><font color="Maroon" title="c1">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</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">definite</a> <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">loc</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font>;<br/><b>let </b><font color="Maroon" title="c5">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:78"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">loc</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">h</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c4">loc</font>;<br/>

<b>assume </b><a NAME="E2:78"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c6">h</font> <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="c3">S</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c7">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>;<br/>

<b>assume </b><a NAME="E3:78"/><i><font color="Green" title="E39">A3</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c4">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c6">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s</font>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <b>means </b> <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s</font>,$1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>;<br/>
<a NAME="E4:78"/><i><font color="Green" title="E40">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<b>by </b><i><a class="ref" href="ami_1.html#T13" target="_self" title="AMI_1:th.13">Tx0</a></i>;<br/>
<div><i><font color="Green" title="E41">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:78_1"/><i><font color="Green" title="E42">A6</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font>]
 ;<br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" target="_self" title="AMI_1:th.14">Tx1</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c7">s</font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:78"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="ami_1.html#E2:78"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="ami_1.html#E3:78"><i><font color="Green" title="E39">A3</font></i></a>, <a class="txt" href="ami_1.html#E1:78_1"><i><font color="Green" title="E42">A6</font></i></a>, <a class="ref" href="ami_1.html#T64" target="_self" title="AMI_1:th.64">Th64</a></i>
<br/>.= 
<font color="Maroon" title="c7">s</font>
<b>by </b><i><a class="ref" href="ami_1.html#D8" target="_self" title="AMI_1:def.8">Def8</a></i>
;<br/><b>hence </b><a NAME="E3:78_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E6:78"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="ami_1.html#E4:78"><i><font color="Green" title="E40">A4</font></i></a>, <a class="txt" href="ami_1.html#E5:78"><i><font color="Green" title="E41">A5</font></i></a>);</i><br/>


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