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 COMPOS_1:125;
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, EXTPRO_1:23
.= card I by A1, A2, Th43, I1 ; :: thesis: verum