let s be State of SCMPDS ; :: thesis: for I being halt-free Program of SCMPDS
for j being shiftable parahalting Instruction 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 halt-free Program of SCMPDS ; :: thesis: for j being shiftable parahalting Instruction 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 shiftable parahalting Instruction 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 ) )
set Mj = Load j;
A1: ( Load j is_closed_on IExec I,s & Load 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 )
then ( I ';' (Load j) is_closed_on s & I ';' (Load j) is_halting_on s ) by A1, SCMPDS_7:43;
hence ( I ';' j is_closed_on s & I ';' j is_halting_on s ) by SCMPDS_4:def 5; :: thesis: verum