(** *** Order *)

Lemma filterlim_le :
forall {T F} {FF : ProperFilter' F} (f g : T -> R) (lf lg : Rbar),
F (fun x => f x <= g x) ->
filterlim f F (Rbar_locally lf) ->
filterlim g F (Rbar_locally lg) ->
Rbar_le lf lg.