Definition is_filter_lim (F : (T -> Prop) -> Prop) (x : T) :=
  forall P, locally x P -> F P.

Lemma filterlim_const : forall {T} {U : UniformSpace} {F : (T -> Prop) -> Prop} {FF : Filter F}, forall a : U, filterlim (fun _ => a) F (locally a).