let a be Int_position ; :: thesis: for s being State of SCMPDS
for I being halt-free Program of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS st I is_closed_on s & I is_halting_on s holds
(IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let s be State of SCMPDS ; :: thesis: for I being halt-free Program of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS st I is_closed_on s & I is_halting_on s holds
(IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let I be halt-free Program of SCMPDS ; :: thesis: for j being shiftable parahalting Instruction of SCMPDS st I is_closed_on s & I is_halting_on s holds
(IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
let j be shiftable parahalting Instruction of SCMPDS ; :: thesis: ( I is_closed_on s & I is_halting_on s implies (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a )
assume that
A1: I is_closed_on s and
A2: I is_halting_on s ; :: thesis: (IExec (I ';' j),s) . a = (Exec j,(IExec I,s)) . a
set Mj = Load j;
A3: 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 SCMPDS_5:40;
then A4: DataPart (Initialize (IExec I,s)) = DataPart (IExec I,s) by SCMPDS_4:23;
A5: Load j is_halting_on IExec I,s by SCMPDS_6:35;
Load j is_closed_on IExec I,s by SCMPDS_6:34;
hence (IExec (I ';' j),s) . a = (IExec (Load j),(IExec I,s)) . a by A1, A2, A5, Th49
.= (Exec j,(Initialize (IExec I,s))) . a by SCMPDS_5:45
.= (DataPart (Exec j,(Initialize (IExec I,s)))) . a by A3, FUNCT_1:72, SCMPDS_2:100
.= (DataPart (Exec j,(IExec I,s))) . a by A4, SCMPDS_5:44
.= (Exec j,(IExec I,s)) . a by A3, FUNCT_1:72, SCMPDS_2:100 ;
:: thesis: verum