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