End norm_RInt.
(** * Specific Normed Modules *)
(** Pairs *)
Section prod.
Context {U V : NormedModule R_AbsRing}.

Lemma RInt_fct_extend_pair
(U_RInt : (R -> U) -> R -> R -> U) (V_RInt : (R -> V) -> R -> R -> V) :
(forall f a b l, is_RInt f a b l -> U_RInt f a b = l)
-> (forall f a b l, is_RInt f a b l -> V_RInt f a b = l)
-> forall f a b l, is_RInt f a b l
-> (U_RInt (fun t => fst (f t)) a b, V_RInt (fun t => snd (f t)) a b) = l.