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 ((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 Th20;

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 Th17

.= (IExec ((Macro j),p,(IExec (I,p,s)))) . f by A1, FUNCT_4:11

.= (Exec (j,(Initialized (IExec (I,p,s))))) . f by SCMFSA6C:5

.= (DataPart (Exec (j,(Initialized (IExec (I,p,s)))))) . f by A3, FUNCT_1:49

.= (DataPart (Exec (j,(IExec (I,p,s))))) . f by A2, SCMFSA6C:4

.= (Exec (j,(IExec (I,p,s)))) . f by A3, FUNCT_1:49 ; :: thesis: verum

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 ((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 Th20;

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 Th17

.= (IExec ((Macro j),p,(IExec (I,p,s)))) . f by A1, FUNCT_4:11

.= (Exec (j,(Initialized (IExec (I,p,s))))) . f by SCMFSA6C:5

.= (DataPart (Exec (j,(Initialized (IExec (I,p,s)))))) . f by A3, FUNCT_1:49

.= (DataPart (Exec (j,(IExec (I,p,s))))) . f by A2, SCMFSA6C:4

.= (Exec (j,(IExec (I,p,s)))) . f by A3, FUNCT_1:49 ; :: thesis: verum