let P be Instruction-Sequence of SCMPDS; :: thesis: for s being State of SCMPDS
for I being 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 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 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 ) )
A1: ( Load j is_closed_on IExec (I,P,(Initialize s)),P & Load 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 ) ; :: 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_7:24;
hence ( I ';' j is_closed_on s,P & I ';' j is_halting_on s,P ) by SCMPDS_4:def 3; :: thesis: verum