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<div class="add">

<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">N</font> being <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/> for <font color="Olive" title="b2">S</font> being 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="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Olive" title="b2">S</font><br/> for <font color="Olive" title="b4">l</font> being   <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="Olive" title="b2">S</font></span>)</span>  st <font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">loc</font> holds <br/>for <font color="Olive" title="b5">h</font> being   <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="Olive" title="b3">loc</font>  st <font color="Olive" title="b5">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="Olive" title="b2">S</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Olive" title="b2">S</font></span>)</span>,<font color="Olive" title="b3">loc</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Olive" title="b4">l</font>,<font color="Olive" title="b5">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being 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/> for <font color="Olive" title="b2">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">l</font> being   <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="Olive" title="b1">S</font></span>)</span>  st <font color="Olive" title="b3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">loc</font> holds <br/>for <font color="Olive" title="b4">h</font> being   <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="Olive" title="b2">loc</font>  st <font color="Olive" title="b4">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="Olive" title="b1">S</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Olive" title="b1">S</font></span>)</span>,<font color="Olive" title="b2">loc</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Olive" title="b3">l</font>,<font color="Olive" title="b4">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">l</font> being   <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>  st <font color="Olive" title="b2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">loc</font> holds <br/>for <font color="Olive" title="b3">h</font> being   <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="Olive" title="b1">loc</font>  st <font color="Olive" title="b3">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> holds <br/><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="Olive" title="b1">loc</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Olive" title="b2">l</font>,<font color="Olive" title="b3">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l</font> being   <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>  st <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">loc</font> holds <br/>for <font color="Olive" title="b2">h</font> being   <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>  st <font color="Olive" title="b2">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> holds <br/><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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Olive" title="b1">l</font>,<font color="Olive" title="b2">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">loc</font> implies for <font color="Olive" title="b1">h</font> being   <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>  st <font color="Olive" title="b1">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> holds <br/><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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b1">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> )</span><br/>









<b>assume </b><a NAME="E1:78"/><i><font color="Green" title="E36">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being   <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>  st <font color="Olive" title="b1">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> holds <br/><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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b1">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies <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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c6">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> )</span><br/>

<b>assume </b><a NAME="E2:78"/><i><font color="Green" title="E37">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c6">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><br/>

<b>thus </b><a NAME="E3:78"/>
<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#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c6">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>proof </b></a><div class="add">

<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>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26" target="_self" title="AMI_1:def.26">AMI_1:def 26</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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#K17" title="AMI_1:func.17">--&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> implies <font color="Maroon" title="c7">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> )</span><br/>

<b>assume </b><a NAME="E1:78_1"/><i><font color="Green" title="E38">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#K17" title="AMI_1:func.17">--&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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a></span><br/>

<b>take </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20" target="_self" title="AMI_1:def.20">AMI_1:def 20</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="c3">S</font></span><br/>

<b>thus </b> <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c7">s</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" target="_self" title="AMI_1:th.13">Tx0</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c3">S</font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:78"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="ami_1.html#E2:78"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="ami_1.html#E1:78_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="ami_1.html#T64" target="_self" title="AMI_1:th.64">Th64</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>


</div>
