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<b>let </b><font color="Maroon">k</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">g</font> be    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</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>assume </b><a NAME="E1:66"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">S</font> is <a href="ami_1.html#V10">realistic</a>
 ;<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="E2:66"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">il</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span> &amp; <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">il</font> )
 ;<br/>

<a NAME="E3:66"/><i><font color="Green">E61</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T63">AMI_5:63</a></i>;<br/>
<b>consider </b><font color="Maroon">i</font> being  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E5:66"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">il</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26">AMISTD_1:26</a></i>;<br/>
<a NAME="E6:66"/>
<font color="Maroon">i</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E7:66"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <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">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> where <font color="Olive">j</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">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span> </span>}</span> 
 
<b>by </b><i>, <a class="txt" href="scmring4.html#E11"><i><font color="Green">Lemma53</font></i></a></i>;<br/>
<a NAME="E8:66"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring4.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E9:66"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">il</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E11"><i><font color="Green">Lemma53</font></i></a>, </i>;<br/>
<a NAME="E10:66"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">il</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> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="amistd_2.html#D15">AMISTD_2:def 15</a></i>;<br/>
<a NAME="E11:66"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">il</font>
 
<b>by </b><i>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E12:66"/>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T63">AMI_5:63</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">il</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">il</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</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> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">il</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
<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> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">il</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">il</font>
<b>by </b><i>, </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="ami_5.html#K6">ProgramPart</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">il</font></span>)</span>,<font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="scmring4.html#T2" target="_self">Th2</a></i>
<br/>.= 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><br/>


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