(** Limits *)

(* Specifications: *)
Lemma is_lim_exp_p : is_lim (fun y => exp y) p_infty p_infty.
Lemma is_lim_exp_m : is_lim (fun y => exp y) m_infty 0.
Lemma ex_lim_exp (x : Rbar) : ex_lim (fun y => exp y) x.
Lemma Lim_exp (x : Rbar) :
Lim (fun y => exp y) x =
match x with
| Finite x => exp x
| p_infty => p_infty
| m_infty => 0
end.
Lemma is_lim_div_exp_p : is_lim (fun y => exp y / y) p_infty p_infty.
Lemma is_lim_mul_exp_m : is_lim (fun y => y * exp y) m_infty 0.
Lemma is_lim_div_expm1_0 : is_lim (fun y => (exp y - 1) / y) 0 1.
(** Integral *)
Lemma is_RInt_exp :
forall a b,
is_RInt exp a b (exp b - exp a).