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

Lemma lt_max_nat_of_N :
forall x y z : BDDvar,
BDDcompare (BDDvar_max x y) z = Datatypes.Lt ->
max (nat_of_N x) (nat_of_N y) < nat_of_N z.