let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being really-closed good InitHalting MacroInstruction of SCM+FSA
for b being Int-Location
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
(IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b

set D = Data-Locations ;
let s be State of SCM+FSA; :: thesis: for I being really-closed good InitHalting MacroInstruction of SCM+FSA
for b being Int-Location
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
(IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b

let I be really-closed good InitHalting MacroInstruction of SCM+FSA ; :: thesis: for b being Int-Location
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
(IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b

let b be Int-Location; :: thesis: for a being read-write Int-Location st not I destroys a & s . a > 0 holds
(IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b

let a be read-write Int-Location; :: thesis: ( not I destroys a & s . a > 0 implies (IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b )
assume A1: ( not I destroys a & s . a > 0 ) ; :: thesis: (IExec ((Times (a,I)),p,s)) . b = (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b
set IT = IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)));
b in Int-Locations by AMI_2:def 16;
then A2: b in Data-Locations by ;
hence (IExec ((Times (a,I)),p,s)) . b = (DataPart (IExec ((Times (a,I)),p,s))) . b by FUNCT_1:49
.= (DataPart (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s))))) . b by
.= (IExec ((Times (a,I)),p,(IExec ((I ";" (SubFrom (a,()))),p,s)))) . b by ;
:: thesis: verum