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;

theorem Th4:
  (Initialize s).a = s.a
proof
  not a in dom SA0 by SCMPDS_4:18;
  hence (Initialize s).a =s.a by FUNCT_4:11;
end;
