let s be State of SCMPDS; :: thesis: for I being Program of SCMPDS
for J being parahalting shiftable Program of SCMPDS st I is_closed_on s & I is_halting_on s holds
( I ';' J is_closed_on s & I ';' J is_halting_on s )
let I be Program of SCMPDS; :: thesis: for J being parahalting shiftable Program of SCMPDS st I is_closed_on s & I is_halting_on s holds
( I ';' J is_closed_on s & I ';' J is_halting_on s )
let J be parahalting shiftable Program of SCMPDS; :: thesis: ( I is_closed_on s & I is_halting_on s implies ( I ';' J is_closed_on s & I ';' J is_halting_on s ) )
A1: ( J is_closed_on IExec (I,s) & J is_halting_on IExec (I,s) ) by SCMPDS_6:34, SCMPDS_6:35;
assume ( I is_closed_on s & I is_halting_on s ) ; :: thesis: ( I ';' J is_closed_on s & I ';' J is_halting_on s )
hence ( I ';' J is_closed_on s & I ';' J is_halting_on s ) by A1, SCMPDS_7:43; :: thesis: verum