theorem Th14:
  for S being OrderSortedSign, X being non-empty ManySortedSet of
  S, x being set holds x is Element of ParsedTermsOSA(X) iff x is Element of TS
  DTConOSA(X)
proof
  let S being OrderSortedSign, X being non-empty ManySortedSet of S, x being
  set;
  TS DTConOSA X = union rng (ParsedTerms X) by Th8
    .= Union (the Sorts of ParsedTermsOSA(X)) by CARD_3:def 4;
  hence thesis;
end;
