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

<b>let </b><font color="Maroon">p</font> be  <a href="ami_1.html#V11">autonomic</a> non <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>



<b>assume </b><a NAME="E1:72"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>set </b><font color="Maroon">Csi</font> = <span class="p1">(<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">i</font>;<br/>
<b>set </b><font color="Maroon">loc</font> =  <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">i</font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">ll</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="E3:72"/><i><font color="Green">E35</font></i>: 
 <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">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <font color="Maroon">ll</font>
 <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">loc1</font> =  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E4:72"/><i><font color="Green">E45</font></i>: 
 <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">i</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a></i>;<br/>
<b>assume </b><a NAME="E5:72"/><i><font color="Green">E52</font></i>: 
not  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6" target="_self">ProgramPart</a> <font color="Maroon">p</font></span>)</span>
 ;<br/>

<a NAME="E6:72"/>
(  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6" target="_self">ProgramPart</a> <font color="Maroon">p</font></span>)</span> iff  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a>  )
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<a NAME="E7:72"/><b>then </b><i><font color="Green">E54</font></i>: 
not  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:72"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">p1</font> = <font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">p2</font> = <font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E8:72"/><i><font color="Green">E55</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E9:72"/><i><font color="Green">E56</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E10:72"/><b>then </b><i><font color="Green">E57</font></i>: 
(  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E11:72"/><b>then </b><i><font color="Green">E58</font></i>: 
(  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <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">i</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">s1</font> being   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E13:72"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39">AMI_3:39</a></i>;<br/>
<b>consider </b><font color="Maroon">s2</font> being   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E15:72"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39">AMI_3:39</a></i>;<br/>
<b>set </b><font color="Maroon">Cs1i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">Cs2i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font>;<br/>
<a NAME="E16:72"/><i><font color="Green">E102</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E17:72"/>
not <font color="Maroon">p</font> is <a href="ami_1.html#V11">autonomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">s1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25">AMI_1:def 25</a><br/>

<b>take </b>
<font color="Maroon">s2</font>
;<br/>

<a NAME="E1:72_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a>  )
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E2:72_1"/><b>then </b><i><font color="Green">E103</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font> )
 
<b>by </b><i><a class="ref" href="ami_3.html#T37">AMI_3:37</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:72_1_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:72_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E3:72_1_1"/><b>then </b>
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i>, <a class="txt" href="ami_5.html#E8:72"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_4.html#T17">FUNCT_4:17</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E4:72_1_1"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:72_1"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font>
 <b>by </b><i><a class="txt" href="ami_5.html#E7:72"><i><font color="Green">E54</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:72_1_2"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:72_1_2"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E3:72_1_2"/><b>then </b>
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="txt" href="ami_5.html#E5:72"><i><font color="Green">E52</font></i></a>, <a class="txt" href="ami_5.html#E9:72"><i><font color="Green">E56</font></i></a>, <a class="ref" href="funct_4.html#T17">FUNCT_4:17</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E4:72_1_2"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:72_1"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="txt" href="ami_5.html#E7:72"><i><font color="Green">E54</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E7:72_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</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">i</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p4">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>
<a NAME="E8:72_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<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">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</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">i</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<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">i</font></span>)</span></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p5">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<a NAME="E9:72_1"/><b>then </b><i><font color="Green">E108</font></i>: 
( <font color="Maroon">s1</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</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">i</font></span>)</span></span>)</span> &amp; <font color="Maroon">s2</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="txt" href="ami_5.html#E5:72"><i><font color="Green">E52</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<b>take </b><font color="Maroon">k</font> = <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1;<br/>

<b>set </b><font color="Maroon">Cs1k</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>;<br/>
<b>set </b><font color="Maroon">Cs2k</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>;<br/>
<i><font color="Green">E109</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>

;<br/>
<i><font color="Green">E110</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>

;<br/>
<a NAME="E12:72_1"/><i><font color="Green">E111</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</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">i</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_5.html#E10:72"><i><font color="Green">E57</font></i></a>, <a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>;<br/>
<a NAME="E13:72_1"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</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">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="ami_5.html#E8:72"><i><font color="Green">E55</font></i></a>, <a class="ref" href="ami_1.html#D25">AMI_1:def 25</a></i>;<br/>
<a NAME="E14:72_1"/><i><font color="Green">E113</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> &amp; <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">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><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">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<a NAME="E15:72_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E8:72"><i><font color="Green">E55</font></i></a>, <a class="txt" href="ami_5.html#E9:72"><i><font color="Green">E56</font></i></a>, <a class="ref" href="ami_1.html#D25">AMI_1:def 25</a></i>;<br/>
<a NAME="E16:72_1"/><b>then </b><i><font color="Green">E114</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</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">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</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">i</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="ami_5.html#T31" target="_self">Th31</a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<a NAME="E17:72_1"/>
(  <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">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</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">i</font></span>)</span></span>)</span> &amp;  <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">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="ami_5.html#T28" target="_self">Th28</a>, </i>;<br/>
<a NAME="E18:72_1"/><b>then </b><i><font color="Green">E115</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</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">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_5.html#E11:72"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_5.html#T27" target="_self">Th27</a>, <a class="ref" href="ami_3.html#T13">AMI_3:13</a></i>;<br/>
<a NAME="E19:72_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<b>hence </b><a NAME="E20:72_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E18:72"/>
contradiction
 ;<br/>


</div>
