let s be State of ; :: thesis: for I being No-StopCode Program of st I is_closed_on s & I is_halting_on s holds
IC (IExec I,s) = inspos (card I)
let I be No-StopCode Program of ; :: thesis: ( I is_closed_on s & I is_halting_on s implies IC (IExec I,s) = inspos (card I) )
set s1 = s +* (Initialized (stop I));
assume that
A1: I is_closed_on s and
A2: I is_halting_on s ; :: thesis: IC (IExec I,s) = inspos (card I)
A3: ProgramPart (s +* (Initialized (stop I))) halts_on s +* (Initialized (stop I)) by A2, Def3;
thus IC (IExec I,s) = IC (Result (s +* (Initialized (stop I)))) by SCMPDS_5:22
.= IC (Computation (s +* (Initialized (stop I))),(LifeSpan (s +* (Initialized (stop I))))) by A3, AMI_1:122
.= inspos (card I) by A1, A2, Th43 ; :: thesis: verum