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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="ami_3.html#M1" target="_self">Data-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1" target="_self">SCM</a> ;<br/>







<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>1</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_2.html#K4">SCM-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="ami_2.html#NM1">SCM-State</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = 7 as    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<a NAME="E6:17"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 
;<br/>
<a NAME="E7:17"/><i><font color="Green">E15</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T5" target="_self">Th5</a></i>;<br/>
<i><font color="Green">E16</font></i>:  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="ami_2.html#K16">SCM-Exec-Res</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="ami_3.html#T7" target="_self">Th7</a></i>
<br/>.= 
 <a href="ami_2.html#K7">SCM-Chg</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K13">cond_address</a> </span>)</span></span>)</span>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K12">cjump_address</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_2.html#K15">Next</a> <span class="p3">(<span class="default"><a href="ami_2.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E6:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="ami_2.html#D16">AMI_2:def 16</a></i>
;<br/>
<b>thus </b><a NAME="E9:17"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 implies <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>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</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> <a href="ami_3.html#K1" target="_self">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:17_2"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K13">cond_address</a> </span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="ami_3.html#E6:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="ami_2.html#T25">AMI_2:25</a></i>;<br/>
<b>thus </b><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>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</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> <a href="ami_3.html#K1" target="_self">SCM</a> </span>)</span> = 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K13">cond_address</a> </span>)</span></span>)</span>,0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K12">cjump_address</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K15">Next</a> <span class="p2">(<span class="default"><a href="ami_2.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E8:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="ami_2.html#T16">AMI_2:16</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K12">cjump_address</a> 
<b>by </b><i><a class="txt" href="ami_3.html#E2:17_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="ami_3.html#E6:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="ami_2.html#T25">AMI_2:25</a></i>
;<br/>


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

<b>thus </b><a NAME="E10:17"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies <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>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</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> <a href="ami_3.html#K1" target="_self">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E2:17_3"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K13">cond_address</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="ami_3.html#E6:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="ami_2.html#T25">AMI_2:25</a></i>;<br/>
<b>thus </b><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>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</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> <a href="ami_3.html#K1" target="_self">SCM</a> </span>)</span> = 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K13">cond_address</a> </span>)</span></span>)</span>,0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_2.html#K12">cjump_address</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K15">Next</a> <span class="p2">(<span class="default"><a href="ami_2.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E8:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="ami_2.html#T16">AMI_2:16</a></i>
<br/>.= 
 <a href="ami_2.html#K15">Next</a> <span class="p1">(<span class="default"><a href="ami_2.html#K6">IC</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E2:17_3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
<br/>.= 
 <a href="ami_3.html#K11" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E7:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="ami_3.html#T6" target="_self">Th6</a></i>
;<br/>


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

<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>thus </b><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>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="ami_3.html#E8:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="ami_2.html#T17">AMI_2:17</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="ami_3.html#K2" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font>

;<br/>


</div>
