<?xml version="1.0"?>
<div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V7" title="AMI_1:attr.7">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  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">d</font> being <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b2">d</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b3">f</font></span><br/><b>let </b><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#V7" title="AMI_1:attr.7">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  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">d</font> being <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b2">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font> holds  <font color="Olive" title="b1">d</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b2">f</font></span><br/><b>let </b><font color="Maroon" title="c3">d</font> be  <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font> holds  <font color="Maroon" title="c3">d</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b1">f</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">d</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">f</font></span><br/>







<a NAME="E1:56"/><i><font color="Green" title="E19">A</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<a NAME="E2:56"/><i><font color="Green" title="E20">B</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">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>
 
<b>by </b><i><a class="ref" href="ami_1.html#T139" title="AMI_1:th.139">AMI_1:139</a></i>;<br/>
<a NAME="E3:56"/>
 <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>
 
<b>by </b><i><a class="ref" href="scmnorm.html#T15" target="_self" title="SCMNORM:th.15">Th15</a></i>;<br/>
<a NAME="E4:56"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">d</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E19">A</font></i></a>, <a class="txt" href="#E2:56"><i><font color="Green" title="E20">B</font></i></a>, <a class="ref" href="xboole_1.html#T64" title="XBOOLE_1:th.64">XBOOLE_1:64</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
<font color="Maroon" title="c3">d</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T138" title="PARTFUN1:th.138">PARTFUN1:138</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
