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
  for s being State of SCMPDS, I,J being Program of SCMPDS holds I
  is_closed_on s,P iff I is_closed_on Initialize s,P+*J
proof
  let s be State of SCMPDS,I,J be Program of SCMPDS;
  DataPart s = DataPart Initialize s by MEMSTR_0:45;
  hence thesis by Th13;
end;
