Definition Majxy (x y:R) (n:nat) : R :=
  Rmax 1 (Rmax (Rabs x) (Rabs y)) ^ (4 * S n) / INR (fact n).

Lemma reste1_maj : forall (x y:R) (N:nat), (0 < N)%nat -> Rabs (Reste1 x y N) <= Majxy x y (pred N).