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

<b>let </b><font color="Maroon">c<sub>2</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>3</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#V8">definite</a> <a href="ami_1.html#V10">realistic</a> <a href="amistd_1.html#V4" target="_self">standard</a>  <a href="ami_1.html#L1">AMI-Struct</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#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:67"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K9" target="_self">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D16" target="_self">AMISTD_1:def 16</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><a NAME="E6:67_1_1"/><i><font color="Green">E37</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#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T65">FUNCT_4:65</a></i>;<br/><a NAME="E7:67_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font> <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#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E8:67_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/><i><font color="Green">E40</font></i>:  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E7:67_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="amistd_1.html#E8:67_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>
;<br/><a NAME="E10:67_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <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#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_1.html#E6:67_1_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>then </b><i><font color="Green">E41</font></i>: <font color="Maroon">c<sub>10</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="amistd_1.html#E8:67_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>
;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span>

<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
 <a href="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="amistd_1.html#E1:67"><i><font color="Green">E34</font></i></a>, <a class="txt" href="amistd_1.html#E9:67_1_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="amistd_1.html#E11:67_1_1"><i><font color="Green">E41</font></i></a></i>
;<br/><b>hence </b><a NAME="E13:67_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</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"><a href="ami_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:67_1_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="amistd_1.html#E9:67_1_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="amistd_1.html#E11:67_1_1"><i><font color="Green">E41</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</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"><a href="ami_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E3:67_1_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><b>thus </b><font color="Maroon">c<sub>6</sub></font> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E3:67_1_2"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
 <a href="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="amistd_1.html#E1:67"><i><font color="Green">E34</font></i></a>, <a class="txt" href="amistd_1.html#E3:67_1_2"><i><font color="Green">E36</font></i></a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:67_1"/>
( <font color="Maroon">c<sub>6</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="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> iff <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</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"><a href="ami_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> ) </span>}</span>  )
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:67_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:67"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</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"> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>3</sub></font> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E4:67"/>
 <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <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="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>


</div>
