let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for s being 0 -started State of SCMPDS
for I being halt-free parahalting Program of SCMPDS st I c= P holds
IC (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = card I
let s be 0 -started State of SCMPDS; :: thesis: for I being halt-free parahalting Program of SCMPDS st I c= P holds
IC (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = card I
let I be halt-free parahalting Program of SCMPDS; :: thesis: ( I c= P implies IC (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = card I )
set ss = s;
set PP = P +* (stop I);
set m = LifeSpan ((P +* (stop I)),s);
A1: stop I c= P +* (stop I) by FUNCT_4:26;
A2: ( (stop I) +* (P +* (stop I)) = P +* (stop I) & (P +* (stop I)) +* (stop I) = P +* (stop I) ) by A1, FUNCT_4:103, FUNCT_4:104;
assume I c= P ; :: thesis: IC (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = card I
then NPP (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = NPP (Comput ((P +* (stop I)),s,(LifeSpan ((P +* (stop I)),s)))) by Th29;
hence IC (Comput (P,s,(LifeSpan ((P +* (stop I)),s)))) = IC (Comput ((P +* (stop I)),s,(LifeSpan ((P +* (stop I)),s)))) by COMPOS_1:230
.= card I by Th27, A2, FUNCT_4:26 ;
:: thesis: verum