let s be State of SCM+FSA; for a being Int-Location
for p being Instruction-Sequence of SCM+FSA
for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),p,s)) . a = (Exec (j,(IExec (I,p,s)))) . a
let a be Int-Location; for p being Instruction-Sequence of SCM+FSA
for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),p,s)) . a = (Exec (j,(IExec (I,p,s)))) . a
let p be Instruction-Sequence of SCM+FSA; for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA
for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),p,s)) . a = (Exec (j,(IExec (I,p,s)))) . a
let I be really-closed InitHalting keepInt0_1 Program of SCM+FSA; for j being sequential Instruction of SCM+FSA holds (IExec ((I ";" j),p,s)) . a = (Exec (j,(IExec (I,p,s)))) . a
let j be sequential Instruction of SCM+FSA; (IExec ((I ";" j),p,s)) . a = (Exec (j,(IExec (I,p,s)))) . a
set Mj = Macro j;
set SA = Start-At (((IC (IExec ((Macro j),p,(IExec (I,p,s))))) + (card I)),SCM+FSA);
A1:
not a in dom (Start-At (((IC (IExec ((Macro j),p,(IExec (I,p,s))))) + (card I)),SCM+FSA))
by SCMFSA_2:102;
A2:
DataPart (Initialized (IExec (I,p,s))) = DataPart (IExec (I,p,s))
by Th20;
a in Int-Locations
by AMI_2:def 16;
then A3:
a in Data-Locations
by SCMFSA_2:100, XBOOLE_0:def 3;
thus (IExec ((I ";" j),p,s)) . a =
(IncIC ((IExec ((Macro j),p,(IExec (I,p,s)))),(card I))) . a
by Th17
.=
(IExec ((Macro j),p,(IExec (I,p,s)))) . a
by A1, FUNCT_4:11
.=
(Exec (j,(Initialized (IExec (I,p,s))))) . a
by SCMFSA6C:5
.=
(DataPart (Exec (j,(Initialized (IExec (I,p,s)))))) . a
by A3, FUNCT_1:49
.=
(DataPart (Exec (j,(IExec (I,p,s))))) . a
by A2, SCMFSA6C:4
.=
(Exec (j,(IExec (I,p,s)))) . a
by A3, FUNCT_1:49
; verum