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