pairwise_disjoint_on_Ioc_pred — Mathlib

English

If α is a linear pred order, f is antitone, then the intervals Ioc (f n) (f (pred n)) are pairwise disjoint.

Русский

Для линейного предпорядка и антитонной f интервалы Ioc (f n) (f(pred n)) попарно непересекаются.

LaTeX

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

Lean4

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

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