(** ** Limits expressed with filters *)

Definition filter_le {T : Type} (F G : (T -> Prop) -> Prop) :=
  forall P, G P -> F P.

(* Specifications: *)
Lemma filter_le_refl : forall T F, @filter_le T F F.
Lemma filter_le_trans : forall T F G H, @filter_le T F G -> filter_le G H -> filter_le F H.