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

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