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).

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Lemma Vn_Un_Wn_order :
forall (Un:nat -> R) (pr1:has_ub Un) (pr2:has_lb Un)
(n:nat), sequence_lb Un pr2 n <= Un n <= sequence_ub Un pr1 n.