let f be FinSeq-Location ; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: (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 ; :: thesis: verum