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).