let s be State of SCMPDS ; :: thesis: for I being halt-free Program of SCMPDS st I is_closed_on s & I is_halting_on s holds
IC (IExec I,s) = card I
let I be halt-free Program of SCMPDS ; :: thesis: ( I is_closed_on s & I is_halting_on s implies IC (IExec I,s) = card I )
set s1 = (Initialize s) +* (stop I);
I1: (Initialize s) +* (stop I) = s +* (Initialize (stop I)) by SCMPDS_4:5;
assume that
A1: I is_closed_on s and
A2: I is_halting_on s ; :: thesis: IC (IExec I,s) = card I
A3: ProgramPart ((Initialize s) +* (stop I)) halts_on (Initialize s) +* (stop I) by A2, Def3;
thus IC (IExec I,s) = IC (Result (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I))) by SCMPDS_5:22
.= IC (Comput (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) by A3, AMI_1:122
.= card I by A1, A2, Th43, I1 ; :: thesis: verum