Definition sequence_ub (Un:nat -> R) (pr:has_ub Un)
(i:nat) : R := lub (fun k:nat => Un (i + k)%nat) (maj_ss Un i pr).
Definition sequence_lb (Un:nat -> R) (pr:has_lb Un)
(i:nat) : R := glb (fun k:nat => Un (i + k)%nat) (min_ss Un i pr).
(* Compatibility *)
Notation sequence_majorant := sequence_ub (only parsing).
Notation sequence_minorant := sequence_lb (only parsing).

Lemma maj_min :
forall (Un:nat -> R) (pr1:has_ub Un) (pr2:has_lb Un),
has_lb (sequence_ub Un pr1).