let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for s being 0 -started State of SCMPDS
for I being parahalting Program of SCMPDS
for J being Program of SCMPDS st stop I c= P holds
for m being Element of NAT st m <= LifeSpan (P,s) holds
NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m))
let s be 0 -started State of SCMPDS; :: thesis: for I being parahalting Program of SCMPDS
for J being Program of SCMPDS st stop I c= P holds
for m being Element of NAT st m <= LifeSpan (P,s) holds
NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m))
let I be parahalting Program of SCMPDS; :: thesis: for J being Program of SCMPDS st stop I c= P holds
for m being Element of NAT st m <= LifeSpan (P,s) holds
NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m))
let J be Program of SCMPDS; :: thesis: ( stop I c= P implies for m being Element of NAT st m <= LifeSpan (P,s) holds
NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m)) )
assume A1: stop I c= P ; :: thesis: for m being Element of NAT st m <= LifeSpan (P,s) holds
NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m))
set sIJ = stop (I ';' J);
set SS = Stop SCMPDS;
let m be Element of NAT ; :: thesis: ( m <= LifeSpan (P,s) implies NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m)) )
assume A2: m <= LifeSpan (P,s) ; :: thesis: NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m))
P +* (stop (I ';' J)) = P +* (I ';' (J ';' (Stop SCMPDS))) by AFINSQ_1:30;
hence NPP (Comput (P,s,m)) = NPP (Comput ((P +* (stop (I ';' J))),s,m)) by A1, A2, Th23; :: thesis: verum