
theorem ThRankDL:
  for L being RATional positive-definite Z_Lattice holds
  rank(L) = rank(DualLat(L))
  proof
    let L be RATional positive-definite Z_Lattice;
    set I = the Basis of EMLat(L);
    DualBasis(I) is Basis of DualLat(L) by ThDLDB;
    then rank DualLat(L) = card DualBasis(I) by ZMODUL03:def 5
    .= card I by ThDB1
    .= rank EMLat(L) by ZMODUL03:def 5;
    hence thesis by ZMODLAT2:42;
  end;
