let s be State of SCMPDS ; :: thesis: for I being parahalting No-StopCode Program of SCMPDS 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 SCMPDS ; :: 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)));
assume A1: Initialized I c= s ; :: thesis: IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
A2: Initialized (stop I) c= s +* (Initialized (stop I)) by FUNCT_4:26;
thus IC (Computation s,(LifeSpan (s +* (Initialized (stop I))))) = IC (Computation (s +* (Initialized (stop I))),(LifeSpan (s +* (Initialized (stop I))))) by A1, Th29, AMI_1:121
.= IC (Computation (s +* (Initialized (stop I))),(LifeSpan ((s +* (Initialized (stop I))) +* (Initialized (stop I))))) by A2, FUNCT_4:79
.= inspos (card I) by Th27, FUNCT_4:26 ; :: thesis: verum