let s be State of SCM+FSA; :: thesis: 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; :: 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)) . a = (Exec (j,(IExec (I,p,s)))) . a

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)) . a = (Exec (j,(IExec (I,p,s)))) . a

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)) . a = (Exec (j,(IExec (I,p,s)))) . a

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

let a be Int-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)) . a = (Exec (j,(IExec (I,p,s)))) . a

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)) . a = (Exec (j,(IExec (I,p,s)))) . a

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)) . a = (Exec (j,(IExec (I,p,s)))) . a

let j be sequential Instruction of SCM+FSA; :: thesis: (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 ; :: thesis: verum