Definition t:=N.Definition eq:=@eq N.Definition eq_refl := @refl_equal t.Definition eq_sym := @sym_eq t.Definition eq_trans := @trans_eq t.Definition lt p q:= Nless p q = true.Definition lt_trans := Nless_trans.

(* Specifications: *)
Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y.