Definition BDDvar_le := Nleb.Definition BDDvar_max (x y : BDDvar) := if BDDvar_le x y then y else x.

Lemma le_nat_of_N_max : forall x y z : BDDvar, BDDvar_le x (BDDvar_max y z) = true -> nat_of_N x <= max (nat_of_N y) (nat_of_N z).