let s be State of ; :: thesis: for I being No-StopCode Program of
for J being Program of st I c= J & I is_closed_on s & I is_halting_on s holds
IC (Computation (s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
let I be No-StopCode Program of ; :: thesis: for J being Program of st I c= J & I is_closed_on s & I is_halting_on s holds
IC (Computation (s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
let J be Program of ; :: thesis: ( I c= J & I is_closed_on s & I is_halting_on s implies IC (Computation (s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I) )
set s1 = s +* (Initialized J);
set ss = s +* (Initialized (stop I));
set m = LifeSpan (s +* (Initialized (stop I)));
assume that
A1: I c= J and
A2: I is_closed_on s and
A3: I is_halting_on s ; :: thesis: IC (Computation (s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = inspos (card I)
thus IC (Computation (s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = IC (Computation (s +* (Initialized (stop I))),(LifeSpan (s +* (Initialized (stop I))))) by A1, A2, A3, Th39, AMI_1:121
.= inspos (card I) by A2, A3, SCMPDS_6:43 ; :: thesis: verum