let a be Int_position ; :: thesis: for P being the Instructions of SCMPDS -valued ManySortedSet of NAT
for s being 0 -started State of SCMPDS
for I being halt-free parahalting Program of SCMPDS
for J being parahalting shiftable Program of SCMPDS holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for s being 0 -started State of SCMPDS
for I being halt-free parahalting Program of SCMPDS
for J being parahalting shiftable Program of SCMPDS holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let s be 0 -started State of SCMPDS; :: thesis: for I being halt-free parahalting Program of SCMPDS
for J being parahalting shiftable Program of SCMPDS holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let I be halt-free parahalting Program of SCMPDS; :: thesis: for J being parahalting shiftable Program of SCMPDS holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let J be parahalting shiftable Program of SCMPDS; :: thesis: (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
A1: not a in dom (Start-At (((IC (IExec (J,P,(IExec (I,P,s))))) + (card I)),SCMPDS)) by SCMPDS_4:59;
IExec ((I ';' J),P,s) = IncIC ((IExec (J,P,(IExec (I,P,s)))),(card I)) by Th38;
hence (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a by A1, FUNCT_4:12; :: thesis: verum