let s be 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,s) & J is_halting_on IExec (I,s) holds
(IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,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,s) & J is_halting_on IExec (I,s) holds
(IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,s)))) . a
let J be shiftable Program of SCMPDS; :: thesis: for a being Int_position st J is_closed_on IExec (I,s) & J is_halting_on IExec (I,s) holds
(IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,s)))) . a
let a be Int_position ; :: thesis: ( J is_closed_on IExec (I,s) & J is_halting_on IExec (I,s) implies (IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,s)))) . a )
A1: ( I is_closed_on s & I is_halting_on s ) by SCMPDS_6:34, SCMPDS_6:35;
assume ( J is_closed_on IExec (I,s) & J is_halting_on IExec (I,s) ) ; :: thesis: (IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,s)))) . a
hence (IExec ((I ';' J),s)) . a = (IExec (J,(IExec (I,s)))) . a by A1, SCMPDS_7:49; :: thesis: verum