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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">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="c4">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#V6" title="AMI_1:attr.6">steady-programmed</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c3">N</font>;<br/><b>let </b><font color="Maroon" title="c5">p</font> be  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM7" title="AMI_1:NM.7">FinPartState</a> of <font color="Maroon" title="c4">S</font>;<br/><b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c4">S</font>;<br/>











<b>assume </b><a NAME="E1:181"/><i><font color="Green" title="E70">A1</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s1</font> &amp; <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c8">Cs1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c1">i</font>;<br/>
<b>set </b><font color="Maroon" title="c9">Cs2</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c1">i</font>;<br/>
<div><i><font color="Green" title="E71">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="181_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:181_1"/><i><font color="Green" title="E72">A3</font></i>: 
<font color="Maroon" title="c10">x</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> <font color="Maroon" title="c5">p</font>
 ;<br/><a NAME="E2:181_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">IL</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D40" target="_self" title="AMI_1:def.40">Def40</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">l</font> = <font color="Maroon" title="c10">x</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c4">S</font> <b>by </b><i><a class="txt" href="ami_1.html#E1:181_1"><i><font color="Green" title="E72">A3</font></i></a>, <a class="ref" href="ami_1.html#D4" target="_self" title="AMI_1:def.4">Def4</a></i>;<br/><a NAME="E4:181_1"/><i><font color="Green" title="E73">A4</font></i>: 
<font color="Maroon" title="c6">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c11">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c11">l</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T54" target="_self" title="AMI_1:th.54">Th54</a></i>;<br/><a NAME="E5:181_1"/><i><font color="Green" title="E74">A5</font></i>: 
<font color="Maroon" title="c7">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c11">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c11">l</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T54" target="_self" title="AMI_1:th.54">Th54</a></i>;<br/><a NAME="E6:181_1"/>
<font color="Maroon" title="c5">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:181"><i><font color="Green" title="E70">A1</font></i></a>, <a class="txt" href="ami_1.html#E1:181_1"><i><font color="Green" title="E72">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E7:181_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:181"><i><font color="Green" title="E70">A1</font></i></a>, <a class="txt" href="ami_1.html#E1:181_1"><i><font color="Green" title="E72">A3</font></i></a>, <a class="txt" href="ami_1.html#E4:181_1"><i><font color="Green" title="E73">A4</font></i></a>, <a class="txt" href="ami_1.html#E5:181_1"><i><font color="Green" title="E74">A5</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/></div><b>end;</b></div>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c1">i</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">S</font>
<b>by </b><i><a class="ref" href="ami_1.html#T79" target="_self" title="AMI_1:th.79">Th79</a></i>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c1">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T79" target="_self" title="AMI_1:th.79">Th79</a></i>
;<br/>
<b>hence </b><a NAME="E4:181"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:181"><i><font color="Green" title="E71">A2</font></i></a>, <a class="ref" href="funct_1.html#T166" title="FUNCT_1:th.166">FUNCT_1:166</a></i>;<br/>


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