Definition max (m n : nat) := if leb m n then n else m.

(* Specifications: *)
Lemma lt_max_1_2 : forall x1 y1 x2 y2 : nat, x1 < x2 -> y1 < y2 -> max x1 y1 < max x2 y2.
Lemma lt_max_2 : forall x1 y1 x2 y2 : nat, x1 < y2 -> y1 < y2 -> max x1 y1 < max x2 y2.
Lemma lt_max_12 : forall x1 y1 x2 y2 : nat, x1 < x2 -> y1 < x2 -> max x1 y1 < max x2 y2.
Lemma BDDcompare_eq : forall x y : BDDvar, BDDcompare x y = Datatypes.Eq -> x = y.