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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="ami_1.html#V10" title="AMI_1:attr.10">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">il</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E9">A1</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a><br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:23_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">il</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E3:23_1"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c6">s</font></span>)</span> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">il</font> &amp; <font color="Maroon" title="c6">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c3">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> )
 ;<br/><a NAME="E4:23_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">il</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E3:23_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="amistd_1.html#E1:23"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:23_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:23"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font>;<br/>
<a NAME="E5:23"/>
(  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> &amp;  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c3">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <font color="Maroon" title="c2">S</font> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D11" title="AMI_1:def.11">AMI_1:def 11</a>, <a class="ref" href="ami_1.html#D14" title="AMI_1:def.14">AMI_1:def 14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">f</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">il</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">il</font>,<font color="Maroon" title="c4">i</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="ami_1.html#T58" title="AMI_1:th.58">AMI_1:58</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font>;<br/>
<a NAME="E7:23"/><i><font color="Green" title="E11">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">il</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<a NAME="E8:23"/><b>then </b><i><font color="Green" title="E12">A5</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c7">f</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E9:23"/><i><font color="Green" title="E13">A6</font></i>: 
<font color="Maroon" title="c3">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c7">f</font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E7:23"><i><font color="Green" title="E11">A4</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E10:23"/><i><font color="Green" title="E14">A7</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">il</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/>
<i><font color="Green" title="E15">A8</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> = 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E8:23"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">il</font>
<b>by </b><i><a class="txt" href="amistd_1.html#E10:23"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/>
<i><font color="Green" title="E16">A9</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">il</font>
<b>by </b><i><a class="txt" href="amistd_1.html#E9:23"><i><font color="Green" title="E13">A6</font></i></a>, <a class="txt" href="amistd_1.html#E11:23"><i><font color="Green" title="E15">A8</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="amistd_1.html#E10:23"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E1:23"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="amistd_1.html#E12:23"><i><font color="Green" title="E16">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="txt" href="amistd_1.html#E3:23"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="amistd_1.html#E11:23"><i><font color="Green" title="E15">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E14:23"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">il</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E20"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/>


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