pairwise_disjoint_on_Ioc_succ — Mathlib

English

In any LT-order, a is not IsSuccPrelimit if and only if there exists b with CovBy b a.

Русский

Для любой линейно упорядоченной множества верно: IsSuccPrelimit a отсутствует ⇔ существует b, такой что CovBy b a.

LaTeX

$$$\lnot IsSuccPrelimit(a) \iff \exists b\, CovBy(b,a)$$$

Lean4

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

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