(** Extensionality *)
Section Extensionality.
Context {K : AbsRing} {V : NormedModule K}.

(* Specifications: *)
Lemma is_pseries_ext (a b : nat -> V) (x : K) (l:V) :
(forall n, a n = b n) -> (is_pseries a x l)
-> is_pseries b x l.
Lemma ex_pseries_ext (a b : nat -> V) (x : K) :
(forall n, a n = b n) -> ex_pseries a x
-> ex_pseries b x.
Lemma is_derive_ext_loc :
forall (f g : K -> V) (x : K) (l : V),
locally x (fun t : K => f t = g t) ->
is_derive f x l -> is_derive g x l.
Lemma ex_derive_ext_loc :
forall (f g : K -> V) (x : K),
locally x (fun t : K => f t = g t) ->
ex_derive f x -> ex_derive g x.
Lemma is_derive_ext :
forall (f g : K -> V) (x : K) (l : V),
(forall t : K, f t = g t) ->
is_derive f x l -> is_derive g x l.
Lemma ex_derive_ext :
forall (f g : K -> V) (x : K),
(forall t : K, f t = g t) ->
ex_derive f x -> ex_derive g x.