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

Lemma is_filter_lim_filtermap {T: UniformSpace} {U : UniformSpace} :
forall F x (f : T -> U),
filterlim f (locally x) (locally (f x))
-> is_filter_lim F x
-> is_filter_lim (filtermap f F) (f x).