let P be Instruction-Sequence of SCMPDS; :: thesis: for s being 0 -started State of SCMPDS
for I being halt-free parahalting Program of SCMPDS
for J being shiftable Program of SCMPDS
for a being Int_position st J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P holds
(IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (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 shiftable Program of SCMPDS
for a being Int_position st J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P holds
(IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (IExec (I,P,s))))) . a
let I be halt-free parahalting Program of SCMPDS; :: thesis: for J being shiftable Program of SCMPDS
for a being Int_position st J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P holds
(IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (IExec (I,P,s))))) . a
let J be shiftable Program of SCMPDS; :: thesis: for a being Int_position st J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P holds
(IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (IExec (I,P,s))))) . a
let a be Int_position; :: thesis: ( J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P implies (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (IExec (I,P,s))))) . a )
( I is_closed_on s,P & I is_halting_on s,P ) by SCMPDS_6:20, SCMPDS_6:21;
hence ( J is_closed_on IExec (I,P,s),P & J is_halting_on IExec (I,P,s),P implies (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(Initialize (IExec (I,P,s))))) . a ) by SCMPDS_7:30; :: thesis: verum