let P be Instruction-Sequence of SCMPDS; :: thesis: 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; :: thesis: 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 ; :: thesis: 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 ; :: thesis: ( 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 ; :: thesis: 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; :: thesis: ( m <= LifeSpan (P,s) implies Comput (P,s,m) = Comput ((P +* (stop (I ';' J))),s,m) )
assume A2: m <= LifeSpan (P,s) ; :: thesis: 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; :: thesis: verum