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).