reserve m,n for Nat,
  a for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1 for Integer,
  loc for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

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;
