theorem Th25:
  for s being State of SCMPDS,I being halt-free Program of
  SCMPDS st I is_closed_on s,P & I is_halting_on s,P
   holds IC IExec(I,P,Initialize s) = card I
proof
  let s be State of SCMPDS,I be halt-free Program of SCMPDS;
  set s1=Initialize s, P1 = P +* stop I;
  assume that
A1: I is_closed_on s,P and
A2: I is_halting_on s,P;
A3: P1 halts_on s1 by A2;
  thus IC IExec(I,P,Initialize s) = IC Result(P1,s1)
    .= IC Comput(P1, s1,LifeSpan(P1,s1)) by A3,EXTPRO_1:23
    .= card I by A1,A2,Th20;
end;
