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<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">g</font> be   <a href="ami_1.html#NM7" title="AMI_1:NM.7">FinPartState</a> of <font color="Maroon" title="c3">S</font>;<br/>







<b>assume </b><a NAME="E1:57"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c3">S</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">x</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/>

<a NAME="E2:57"/><i><font color="Green" title="E48">A2</font></i>: 
 <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/>
<a NAME="E3:57"/><i><font color="Green" title="E49">A3</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring4.html#T51" target="_self" title="SCMRING4:th.51">Th51</a></i>;<br/>
<a NAME="E4:57"/><i><font color="Green" title="E50">A4</font></i>: 
 <a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:57"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="scmring4.html#T52" target="_self" title="SCMRING4:th.52">Th52</a></i>;<br/>
<a NAME="E5:57"/>
 <a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</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="c3">S</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:57"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="ami_1.html#D43" title="AMI_1:def.43">AMI_1:def 43</a></i>;<br/>
<a NAME="E6:57"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</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="c3">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:57"><i><font color="Green" title="E49">A3</font></i></a>, <a class="txt" href="scmring4.html#E4:57"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:57"/>
(  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">IC</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font> )
 <b>by </b><i><a class="txt" href="scmring4.html#E2:57"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


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