Definition maj_Reste_E (x y:R) (N:nat) : R :=
  4 *
  (Rmax 1 (Rmax (Rabs x) (Rabs y)) ^ (2 * N) /
    Rsqr (INR (fact (Nat.div2 (pred N))))).

(* Specifications: *)
Lemma div2_double : forall N:nat, Nat.div2 (2 * N) = N.
Lemma div2_S_double : forall N:nat, Nat.div2 (S (2 * N)) = N.
Lemma div2_not_R0 : forall N:nat, (1 < N)%nat -> (0 < Nat.div2 N)%nat.
Lemma Reste_E_maj : forall (x y:R) (N:nat), (0 < N)%nat -> Rabs (Reste_E x y N) <= maj_Reste_E x y N.
Lemma maj_Reste_cv_R0 : forall x y:R, Un_cv (maj_Reste_E x y) 0.
Lemma Reste_E_cv : forall x y:R, Un_cv (Reste_E x y) 0.
Lemma exp_plus : forall x y:R, exp (x + y) = exp x * exp y.
Lemma exp_pos_pos : forall x:R, 0 < x -> 0 < exp x.
Lemma exp_pos : forall x:R, 0 < exp x.
Lemma derivable_pt_lim_exp_0 : derivable_pt_lim exp 0 1.
Lemma derivable_pt_lim_exp : forall x:R, derivable_pt_lim exp x (exp x).