pairwise_disjoint_on_Ioo_succ — Mathlib

English

If f is antitone, intervals Ioo (f n) (f (pred n)) are pairwise disjoint.

Русский

Если f антитонна, интервалы Ioo (f n) (f (pred n)) попарно непересекаются.

LaTeX

$$PairwiseDisjoint( { Ioo (f n) (f (pred n)) } )$$

Lean4

/-- If `α` is a linear succ order, `β` is a preorder, and `f : α → β` is an antitone function, then
the intervals `Set.Ioo (f (Order.succ n)) (f n)` are pairwise disjoint. -/
theorem pairwise_disjoint_on_Ioo_succ [SuccOrder α] [Preorder β] {f : α → β} (hf : Antitone f) :
    Pairwise (Disjoint on fun n => Ioo (f (succ n)) (f n)) :=
  hf.dual_left.pairwise_disjoint_on_Ioo_pred

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