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<b>let </b><font color="Maroon">N</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">S</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="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">il</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font> holds   <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8">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">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:23_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font>
 ;<br/><b>then consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:23_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">n</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">s</font></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">il</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">il</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 ;<br/><a NAME="E4:23_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">il</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:23_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">il</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">n</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="E3:23"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">il</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font>;<br/>
<a NAME="E5:23"/>
(  <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">S</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> &amp;  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">il</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4">Instructions</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a>, <a class="ref" href="ami_1.html#D14">AMI_1:def 14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span>,<font color="Maroon">il</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">il</font>,<font color="Maroon">i</font> as    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="ami_1.html#T58">AMI_1:58</a></i>;<br/>
<b>set </b><font color="Maroon">a</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</font>;<br/>
<a NAME="E7:23"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <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">S</font></span>)</span>,<font color="Maroon">il</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="E8:23"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E9:23"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">il</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E10:23"/><i><font color="Green">E66</font></i>: 
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">il</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/>
<i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</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">S</font></span>)</span> = 
<font color="Maroon">f</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">S</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">il</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>
;<br/>
<i><font color="Green">E68</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</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"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</font></span>)</span></span>)</span> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">il</font>
<b>by </b><i>, , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i>, <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> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">f</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">S</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">n</font>
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E14:23"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font>
 <b>by </b><i/>;<br/>


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