(** An inefficient boolean order on [N]. Please use [N.leb] instead now. *)
Definition Nleb (a b:N) := leb (N.to_nat a) (N.to_nat b).

Lemma Nltb_double_plus_one_mono a b :
Nleb a b = false ->
Nleb (N.succ_double a) (N.succ_double b) = false.