
theorem
  for L being RATional positive-definite Z_Lattice,
      b being OrdBasis of DualLat(L)
  holds GramMatrix(InnerProduct(DualLat(L)), b) is Matrix of dim(L), F_Rat
  proof
    let L be RATional positive-definite Z_Lattice,
        b be OrdBasis of DualLat(L);
A1: the scalar of DualLat(L) = (ScProductDM(L)) || the carrier of DualLat(L)
    by defDualLat;
    A2: DualLat(L) is Submodule of DivisibleMod(L) by ThDL2;
    dim(L) = dim(DualLat(L)) by ThRankDL;
    hence thesis by A1,A2,ThSLGM2;
  end;
