let s be State of ; :: thesis: for I being parahalting No-StopCode Program of st Initialized I c= s holds
IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
let I be parahalting No-StopCode Program of ; :: thesis: ( Initialized I c= s implies IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I) )
set IsI = Initialized (stop I);
set ss = s +* (Initialized (stop I));
set m = LifeSpan (s +* (Initialized (stop I)));
A1: Initialized (stop I) c= s +* (Initialized (stop I)) by FUNCT_4:26;
assume Initialized I c= s ; :: thesis: IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
hence IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = IC (Computation (s +* (Initialized (stop I))),(LifeSpan (s +* (Initialized (stop I))))) by Th29, AMI_1:121
.= IC (Computation (s +* (Initialized (stop I))),(LifeSpan ((s +* (Initialized (stop I))) +* (Initialized (stop I))))) by A1, FUNCT_4:79
.= inspos (card I) by Th27, FUNCT_4:26 ;
:: thesis: verum