let f be FinSeq-Location ; for s being State of SCM+FSA
for P being Instruction-Sequence of SCM+FSA
for I being keeping_0 really-closed parahalting Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),P,s)) . f = (Exec (j,(IExec (I,P,s)))) . f
let s be State of SCM+FSA; for P being Instruction-Sequence of SCM+FSA
for I being keeping_0 really-closed parahalting Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),P,s)) . f = (Exec (j,(IExec (I,P,s)))) . f
let P be Instruction-Sequence of SCM+FSA; for I being keeping_0 really-closed parahalting Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),P,s)) . f = (Exec (j,(IExec (I,P,s)))) . f
let I be keeping_0 really-closed parahalting Program of SCM+FSA; for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),P,s)) . f = (Exec (j,(IExec (I,P,s)))) . f
let j be sequential Instruction of SCM+FSA; (IExec ((I ";" j),P,s)) . f = (Exec (j,(IExec (I,P,s)))) . f
set Mj = Macro j;
set SA = Start-At (((IC (IExec ((Macro j),P,(IExec (I,P,s))))) + (card I)),SCM+FSA);
A1:
not f in dom (Start-At (((IC (IExec ((Macro j),P,(IExec (I,P,s))))) + (card I)),SCM+FSA))
by SCMFSA_2:103;
A2:
DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))
by Lm2;
f in FinSeq-Locations
by SCMFSA_2:def 5;
then A3:
f in Data-Locations
by SCMFSA_2:100, XBOOLE_0:def 3;
thus (IExec ((I ";" j),P,s)) . f =
(IncIC ((IExec ((Macro j),P,(IExec (I,P,s)))),(card I))) . f
by SCMFSA6B:20
.=
(IExec ((Macro j),P,(IExec (I,P,s)))) . f
by A1, FUNCT_4:11
.=
(Exec (j,(Initialized (IExec (I,P,s))))) . f
by Th4
.=
(DataPart (Exec (j,(Initialized (IExec (I,P,s)))))) . f
by A3, FUNCT_1:49
.=
(DataPart (Exec (j,(IExec (I,P,s))))) . f
by A2, Th3
.=
(Exec (j,(IExec (I,P,s)))) . f
by A3, FUNCT_1:49
; verum