reserve V, C, x, a, b for set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve C for finite set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve u, v for Element of SubstLatt (V, C);
reserve s, t, a, b for Element of PFuncs (V,C);
reserve K, L for Element of SubstitutionSet (V, C);

theorem Th19:
  for u being Element of SubstitutionSet (V, C) holds u = FinJoin(
  u, Atom (V, C))
proof
  let u be Element of SubstitutionSet (V, C);
  thus u = FinUnion(u, singleton PFuncs (V, C)) by SETWISEO:58
    .= FinJoin(u, Atom(V, C)) by Th18;
end;
