let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for s being 0 -started State of SCMPDS
for i being No-StopCode parahalting Instruction of SCMPDS
for J being parahalting shiftable Program of SCMPDS
for a being Int_position holds (IExec ((i ';' J),P,s)) . a = (IExec (J,P,(Exec (i,(Initialize s))))) . a
let s be 0 -started State of SCMPDS; :: thesis: for i being No-StopCode parahalting Instruction of SCMPDS
for J being parahalting shiftable Program of SCMPDS
for a being Int_position holds (IExec ((i ';' J),P,s)) . a = (IExec (J,P,(Exec (i,(Initialize s))))) . a
let i be No-StopCode parahalting Instruction of SCMPDS; :: thesis: for J being parahalting shiftable Program of SCMPDS
for a being Int_position holds (IExec ((i ';' J),P,s)) . a = (IExec (J,P,(Exec (i,(Initialize s))))) . a
let J be parahalting shiftable Program of SCMPDS; :: thesis: for a being Int_position holds (IExec ((i ';' J),P,s)) . a = (IExec (J,P,(Exec (i,(Initialize s))))) . a
let a be Int_position ; :: thesis: (IExec ((i ';' J),P,s)) . a = (IExec (J,P,(Exec (i,(Initialize s))))) . a
thus (IExec ((i ';' J),P,s)) . a = (IExec (((Load i) ';' J),P,s)) . a
.= (IExec (J,P,(IExec ((Load i),P,s)))) . a by SCMPDS_5:39
.= (IExec (J,P,(Exec (i,(Initialize s))))) . a by SCMPDS_5:45 ; :: thesis: verum