Section Locally_fct.
Context {T : Type} {U : UniformSpace}.

Lemma filterlimi_locally_close :
forall {F} {FF: ProperFilter F} (f : T -> U -> Prop) l l',
F (fun x => forall y1 y2, f x y1 -> f x y2 -> y1 = y2) ->
filterlimi f F (locally l) ->  filterlimi f F (locally l') ->
close l l'.