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,s & J is_halting_on IExec I,s holds
( I ';' J is_closed_on s & I ';' J is_halting_on s )
let I be parahalting Program of SCMPDS ; :: thesis: for J being shiftable Program of SCMPDS st J is_closed_on IExec I,s & J is_halting_on IExec I,s holds
( I ';' J is_closed_on s & I ';' J is_halting_on s )
let J be shiftable Program of SCMPDS ; :: thesis: ( J is_closed_on IExec I,s & J is_halting_on IExec I,s implies ( I ';' J is_closed_on s & I ';' J is_halting_on s ) )
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: ( 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