
theorem ThDB1:
  for L being RATional positive-definite Z_Lattice,
  I being Basis of EMLat(L) holds
  card I = card DualBasis(I)
  proof
    let L be RATional positive-definite Z_Lattice,
        I be Basis of EMLat(L);
    B2DB(I) is one-to-one & dom B2DB(I) = I & rng B2DB(I) = DualBasis(I)
    by defB2DB;
    hence thesis by CARD_1:5,WELLORD2:def 4;
  end;
