let P be Instruction-Sequence of SCMPDS; for s being 0 -started State of SCMPDS
for I being parahalting Program of
for J being Program of st stop I c= P holds
for m being Nat st m <= LifeSpan (P,s) holds
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
let s be 0 -started State of SCMPDS; for I being parahalting Program of
for J being Program of st stop I c= P holds
for m being Nat st m <= LifeSpan (P,s) holds
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
let I be parahalting Program of ; for J being Program of st stop I c= P holds
for m being Nat st m <= LifeSpan (P,s) holds
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
let J be Program of ; ( stop I c= P implies for m being Nat st m <= LifeSpan (P,s) holds
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m) )
assume A1:
stop I c= P
; for m being Nat st m <= LifeSpan (P,s) holds
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
set sIJ = stop (I ';' J);
set SS = Stop SCMPDS;
let m be Nat; ( m <= LifeSpan (P,s) implies Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m) )
assume A2:
m <= LifeSpan (P,s)
; Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
P +* (stop (I ';' J)) = P +* (I ';' (J ';' (Stop SCMPDS)))
by AFINSQ_1:27;
hence
Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m)
by A1, A2, Th7; verum