let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for s being State of SCMPDS
for I being halt-free Program of SCMPDS
for j being shiftable parahalting Instruction 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; :: thesis: for I being halt-free Program of SCMPDS
for j being shiftable parahalting Instruction 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 halt-free Program of SCMPDS; :: thesis: for j being shiftable parahalting Instruction 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 shiftable parahalting Instruction of SCMPDS; :: thesis: ( 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 ) )
set Mj = Load j;
A1: ( Load j is_closed_on IExec (I,P,s),P & Load j is_halting_on IExec (I,P,s),P ) by SCMPDS_6:34, SCMPDS_6:35;
assume ( I is_closed_on s,P & I is_halting_on s,P ) ; :: thesis: ( I ';' j is_closed_on s,P & I ';' j is_halting_on s,P )
then ( I ';' (Load j) is_closed_on s,P & I ';' (Load j) is_halting_on s,P ) by A1, SCMPDS_7:43;
hence ( I ';' j is_closed_on s,P & I ';' j is_halting_on s,P ) by SCMPDS_4:def 5; :: thesis: verum