let P be Instruction-Sequence of SCMPDS; :: thesis: for s being State of SCMPDS
for I being parahalting Program of SCMPDS
for J being shiftable Program of SCMPDS st J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P holds
( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P )
let s be State of SCMPDS; :: thesis: for I being parahalting Program of SCMPDS
for J being shiftable Program of SCMPDS st J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P holds
( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P )
let I be parahalting Program of SCMPDS; :: thesis: for J being shiftable Program of SCMPDS st J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P holds
( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P )
let J be shiftable Program of SCMPDS; :: thesis: ( J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P implies ( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P ) )
A1: ( I is_closed_on s,P & I is_halting_on s,P ) by SCMPDS_6:20, SCMPDS_6:21;
assume ( J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P ) ; :: thesis: ( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P )
hence ( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P ) by A1, SCMPDS_7:24; :: thesis: verum