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