(** To be equivalent is an equivalence relation *)
Section Equiv.
Context {T : Type} {K : AbsRing} {V : NormedModule K}.

Lemma equiv_carac_1 :
forall {F : (T -> Prop) -> Prop} {FF : Filter F} (f g o : T -> V),
(forall x, f x = plus (g x) (o x)) -> is_domin F g o -> is_equiv F f g.