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<b>let </b><font color="Maroon" title="c1">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="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V8" title="AMISTD_2:attr.8">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_3.html#V1" title="AMI_3:attr.1">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>set </b><font color="Maroon" title="c6">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1;<br/>
<b>set </b><font color="Maroon" title="c7">P</font> = <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font>;<br/>
<b>assume </b><a NAME="E1:128"/>
 <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 ;<br/>

<a NAME="E2:128"/><b>then </b>
 <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/>
<a NAME="E3:128"/><b>then </b><i><font color="Green" title="E72">A1</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>;<br/>
<a NAME="E4:128"/><i><font color="Green" title="E73">A2</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>;<br/>
<a NAME="E5:128"/><i><font color="Green" title="E74">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E6:128"/>
(  <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> &amp;  <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font> )
 
<b>by </b><i><a class="ref" href="amistd_2.html#T54" target="_self" title="AMISTD_2:th.54">Th54</a></i>;<br/>
<a NAME="E7:128"/><b>then </b>
 <a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:128"/><b>then </b><i><font color="Green" title="E75">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E9:128"/><i><font color="Green" title="E76">A5</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c3">F</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="amistd_2.html#E5:128"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="ami_5.html#D5" title="AMI_5:def.5">AMI_5:def 5</a></i>;<br/>
<a NAME="E10:128"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T50" target="_self" title="AMISTD_2:th.50">Th50</a></i>;<br/>
<a NAME="E11:128"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E12:128"/><b>then </b><i><font color="Green" title="E77">A6</font></i>: 
not  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<i><font color="Green" title="E78">A7</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E12:128"><i><font color="Green" title="E77">A6</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">f</font> = 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="amistd_2.html#E4:128"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="amistd_2.html#E5:128"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="amistd_2.html#E8:128"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="amistd_2.html#E9:128"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="amistd_2.html#E13:128"><i><font color="Green" title="E78">A7</font></i></a>, <a class="ref" href="ami_5.html#D5" title="AMI_5:def.5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:128"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="amistd_2.html#E4:128"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="amistd_2.html#E8:128"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
;<br/>


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