reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem Th18:
  for s being 0-started State of SCMPDS
  for I being parahalting Program of SCMPDS,J being Program of SCMPDS,
      k being Nat st k <= LifeSpan(P +* stop I,s)
  holds  Comput(P +* stop I, s,k) =  Comput(P+*stop(I ';' J),s,k)
proof
  let s be 0-started State of SCMPDS;
  let I be parahalting Program of SCMPDS,J be Program of SCMPDS,
      k be Nat;
A1: stop (I ';' J) = (I ';' (J ';' Stop SCMPDS)) by AFINSQ_1:27;
  thus thesis by A1,Th17;
end;
