
theorem ThDL1:
  for L being RATional positive-definite Z_Lattice,
  v being Vector of DivisibleMod(L) holds
  v in DualLat(L) iff v is Dual of L
  proof
    let L be RATional positive-definite Z_Lattice,
    v be Vector of DivisibleMod(L);
    hereby
      assume v in DualLat(L);
      then v in DualSet L by defDualLat;
      then consider x be Dual of L such that
      A1: x = v;
      thus v is Dual of L by A1;
    end;
    assume v is Dual of L;
    then v in DualSet L;
    hence v in DualLat(L) by defDualLat;
  end;
