Lemma is_derive_RInt_param_bound_comp_aux2 : forall (f : R -> R -> R) (a : R -> R) (b x da : R), (locally x (fun y : R => ex_RInt (fun t => f y t) (a x) b)) -> (exists eps:posreal, locally x (fun y : R => ex_RInt (fun t => f y t) (a x - eps) (a x + eps))) -> is_derive a x da -> (exists eps:posreal, locally x (fun x0 : R => forall t : R, Rmin (a x-eps) b <= t <= Rmax (a x+eps) b -> ex_derive (fun u : R => f u t) x0)) -> (forall t : R, Rmin (a x) b <= t <= Rmax (a x) b -> continuity_2d_pt (fun u v : R => Derive (fun z : R => f z v) u) x t) -> (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_pt (fun t => f x t) (a x) -> is_derive (fun x : R => RInt (fun t => f x t) (a x) b) x (RInt (fun t : R => Derive (fun u => f u t) x) (a x) b+(-f x (a x))*da).