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 f being FinSeq-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((Times (a,I)),p,s)) . f = s . f
set D = Data-Locations ;
let s be State of SCM+FSA; :: thesis: for I being really-closed good InitHalting MacroInstruction of SCM+FSA
for f being FinSeq-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((Times (a,I)),p,s)) . f = s . f
let I be really-closed good InitHalting MacroInstruction of SCM+FSA ; :: thesis: for f being FinSeq-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((Times (a,I)),p,s)) . f = s . f
let f be FinSeq-Location ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds
(IExec ((Times (a,I)),p,s)) . f = s . f
let a be read-write Int-Location; :: thesis: ( s . a <= 0 implies (IExec ((Times (a,I)),p,s)) . f = s . f )
assume A1: s . a <= 0 ; :: thesis: (IExec ((Times (a,I)),p,s)) . f = s . f
set s0 = Initialized s;
set p0 = p;
A2: ( (Initialized s) . a = s . a & (Initialized s) . (intloc 0) = 1 ) by SCMFSA_M:9, SCMFSA_M:37;
f in FinSeq-Locations by SCMFSA_2:def 5;
then A3: f in Data-Locations by SCMFSA_2:100, XBOOLE_0:def 3;
DataPart (IExec ((Times (a,I)),p,s)) = DataPart (IExec ((Times (a,I)),p,(Initialized s))) by SCMFSA8C:3
.= DataPart (Initialized s) by A1, A2, Th47 ;
hence (IExec ((Times (a,I)),p,s)) . f = (DataPart (Initialized s)) . f by A3, FUNCT_1:49
.= (Initialized s) . f by A3, FUNCT_1:49
.= s . f by SCMFSA_M:37 ;
:: thesis: verum