let s be State of SCMPDS ; :: thesis: for I being parahalting No-StopCode 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 parahalting No-StopCode 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