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<b>let </b><font color="Maroon">i</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><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="amistd_1.html#V4">standard</a> <a href="amistd_2.html#V8">regular</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">p</font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font>;<br/>







<b>set </b><font color="Maroon">f</font> =  <a href="amistd_2.html#K10">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="amistd_2.html#K9">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font>;<br/>
<a NAME="E1:65"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D15">AMISTD_2:def 15</a></i>;<br/>
<b>then </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> = 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> </span>}</span> 
<b>by </b><i><a class="ref" href="amistd_2.html#D16">AMISTD_2:def 16</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D16">AMISTD_2:def 16</a></i>
;<br/>
<a NAME="E3:65"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D15">AMISTD_2:def 15</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:65_2"/><i><font color="Green">E57</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/><b>assume </b><a NAME="E2:65_2"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="scmring4.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E4:65_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> </span>}</span> 
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D16">AMISTD_2:def 16</a></i>;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:65_2"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> &amp;  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> )
 ;<br/><a NAME="E7:65_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">i</font>
 <b>by </b><i>, </i>;<br/><a NAME="E8:65_2"/><i><font color="Green">E74</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D15">AMISTD_2:def 15</a></i>;<br/><a NAME="E9:65_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Olive">mm</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span> where <font color="Olive">mm</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">mm</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="amistd_2.html#D16">AMISTD_2:def 16</a></i>;<br/><a NAME="E10:65_2"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">x'</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, </i>;<br/><i><font color="Green">E77</font></i>:  <a href="ami_5.html#K5">pi</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> = 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">x'</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
<b>by </b><i>, <a class="txt" href="scmring4.html#E11"><i><font color="Green">Lemma53</font></i></a>, </i>
<br/>.= 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">x'</font></span>)</span>,<font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="scmring4.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="scmring4.html#T2" target="_self">Th2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:65"/>
 <a href="amistd_2.html#K10">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K9">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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