let s be State of SCM+FSA; :: thesis: for f being FinSeq-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)) . f = (Exec (j,(IExec (I,p,s)))) . f

let f be FinSeq-Location ; :: thesis: 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)) . f = (Exec (j,(IExec (I,p,s)))) . f

let p be Instruction-Sequence of SCM+FSA; :: thesis: 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)) . f = (Exec (j,(IExec (I,p,s)))) . f

let I be really-closed InitHalting keepInt0_1 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 ((),p,(IExec (I,p,s))))) + (card I)),SCM+FSA);
A1: not f in dom (Start-At (((IC (IExec ((),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 Th20;
f in FinSeq-Locations by SCMFSA_2:def 5;
then A3: f in Data-Locations by ;
thus (IExec ((I ";" j),p,s)) . f = (IncIC ((IExec ((),p,(IExec (I,p,s)))),(card I))) . f by Th17
.= (IExec ((),p,(IExec (I,p,s)))) . f by
.= (Exec (j,(Initialized (IExec (I,p,s))))) . f by SCMFSA6C:5
.= (DataPart (Exec (j,(Initialized (IExec (I,p,s)))))) . f by
.= (DataPart (Exec (j,(IExec (I,p,s))))) . f by
.= (Exec (j,(IExec (I,p,s)))) . f by ; :: thesis: verum