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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V7">steady-programmed</a> <a href="ami_1.html#V8">definite</a> <a href="ami_1.html#V10">realistic</a> <a href="amistd_2.html#V13">Exec-preserving</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E1:18"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/>
<a NAME="E2:18"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green">E17</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E4:18"/><i><font color="Green">E18</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E5:18"/><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E6:18"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T41">XBOOLE_1:41</a></i>;<br/>
<a NAME="E7:18"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>;<br/>
<a NAME="E8:18"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:18_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:18_1"/><b>then </b>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/>
<b>hence </b><a NAME="E4:18_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:18_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:18"/><b>then </b><i><font color="Green">E21</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E7:18"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E10:18"/>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="txt" href="scmring4.html#E13"><i><font color="Green">Lemma9</font></i></a></i>;<br/>
<a NAME="E11:18"/><b>then </b><i><font color="Green">E22</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E12"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E12:18"/>
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#R1">misses</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_2"/>
not <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#R1">misses</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:18_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>and </b><br/><a NAME="E4:18_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E5:18_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:18_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_2_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="scmring4.html#E5:18_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_2_1_1"><b>suppose </b></a><a NAME="E1:18_2_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:18_2_1_1"/><b>then </b>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E3:18_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring4.html#E4:18_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_2_1_2"><b>suppose </b></a><a NAME="E1:18_2_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:18_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring4.html#E4:18_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E13:18"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</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#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E14:18"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:18_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E2:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="scmring4.html#E3:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmring4.html#E9:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmring4.html#E13:18"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_4.html#T76">FUNCT_4:76</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/>


</div><b>end;</b></div>
<a NAME="E15:18"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D19">AMISTD_2:def 19</a></i>;<br/>
<i><font color="Green">E25</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E13:18"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_4.html#T76">FUNCT_4:76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E4:18"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scmring4.html#E5:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmring4.html#E9:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmring4.html#E15:18"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a></i>
;<br/>
<i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T5">SCMFSA_3:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T5">SCMFSA_3:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
;<br/>
<b>thus </b> <a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E5:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmring4.html#E11:18"><i><font color="Green">E22</font></i></a>, <a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E16:18"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmring4.html#E17:18"><i><font color="Green">E26</font></i></a>, <a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</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#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E11:18"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
;<br/>


</div>
