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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being 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#V4" title="AMI_1:attr.4">halting</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="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">k</font> being   <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/> for <font color="Olive" title="b3">d</font> being  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Olive" title="b1">S</font> holds   <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Olive" title="b3">d</font>,<font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">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#V4" title="AMI_1:attr.4">halting</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="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <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/> for <font color="Olive" title="b2">d</font> being  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font> holds   <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Olive" title="b2">d</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">k</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font> holds   <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">d</font> be   <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>







<a NAME="E1:39"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">d</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">d</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E2:39"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T139" title="AMI_1:th.139">AMI_1:139</a></span>;<br/>
<a NAME="E3:39"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmnorm.html#T15" target="_self" title="SCMNORM:th.15">Th15</a></span>;<br/>
<a NAME="E4:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">d</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></span>;<br/>
<a NAME="E5:39"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">d</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T134" title="AMI_1:th.134">AMI_1:134</a></span>;<br/>
<a NAME="E6:39"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:39"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">IncrIC</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T95" title="RELAT_1:th.95">RELAT_1:95</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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