let a be Int_position ; :: thesis: for s being State of SCMPDS
for I being halt-free parahalting Program of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS holds (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let s be State of SCMPDS ; :: thesis: for I being halt-free parahalting Program of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS holds (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let I be halt-free parahalting Program of SCMPDS ; :: thesis: for j being shiftable parahalting Instruction of SCMPDS holds (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let j be shiftable parahalting Instruction of SCMPDS ; :: thesis: (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
set Mj = Load j;
set SA = Start-At ((IC (IExec (Load j),(IExec I,s))) + (card I)),SCMPDS ;
A1: not a in dom (Start-At ((IC (IExec (Load j),(IExec I,s))) + (card I)),SCMPDS ) by SCMPDS_4:59;
A2: a in SCM-Data-Loc by SCMPDS_2:def 2;
for a being Int_position holds (Initialize (IExec I,s)) . a = (IExec I,s) . a by Th40;
then A3: DataPart (Initialize (IExec I,s)) = DataPart (IExec I,s) by SCMPDS_4:23;
thus (IExec (I ';' j),s) . a = ((IExec (Load j),(IExec I,s)) +* (Start-At ((IC (IExec (Load j),(IExec I,s))) + (card I)),SCMPDS )) . a by Th38
.= (IExec (Load j),(IExec I,s)) . a by A1, FUNCT_4:12
.= (Exec j,(Initialize (IExec I,s))) . a by Th45
.= (DataPart (Exec j,(Initialize (IExec I,s)))) . a by A2, FUNCT_1:72, SCMPDS_2:100
.= (DataPart (Exec j,(IExec I,s))) . a by A3, Th44
.= (Exec j,(IExec I,s)) . a by A2, FUNCT_1:72, SCMPDS_2:100 ; :: thesis: verum