End RInt_comp.
(** * Parametric integrals *)

Lemma is_derive_RInt_param_aux : forall (f : R -> R -> R) (a b x : R),
locally x (fun x : R => forall t, Rmin a b <= t <= Rmax a b -> ex_derive (fun u : R => f u t) x) ->
(forall t, Rmin a b <= t <= Rmax a b -> continuity_2d_pt (fun u v => Derive (fun z => f z v) u) x t) ->
locally x (fun y : R => ex_RInt (fun t => f y t) a b) ->
ex_RInt (fun t => Derive (fun u => f u t) x) a b ->
is_derive (fun x : R => RInt (fun t => f x t) a b) x
(RInt (fun t => Derive (fun u => f u t) x) a b).