End RInt_comp.
(** * Parametric integrals *)

Lemma is_derive_RInt_param_bound_comp_aux1 :
forall (f : R -> R -> R) (a : R -> R) (x : R),
(exists eps:posreal, locally x (fun y : R => ex_RInt (fun t => f y t) (a x - eps) (a x + eps))) ->
(exists eps:posreal, locally x
(fun x0 : R =>
forall t : R,
a x-eps <= t <= a x+eps ->
ex_derive (fun u : R => f u t) x0)) ->
(locally_2d (fun x' t =>
continuity_2d_pt (fun u v : R => Derive (fun z : R => f z v) u) x' t) x (a x)) ->
continuity_2d_pt
(fun u v : R => Derive (fun z : R => RInt (fun t : R => f z t) v (a x)) u) x (a x).