IsSuccPrelimit — Mathlib

English

If f is antitone on a linear pred order, the Ico (f n) (f (pred n)) sets are pairwise disjoint.

Русский

Если f антитонна на линейном предпорядке, интервалы Ico (f n) (f (pred n)) попарно непересекаются.

LaTeX

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

Lean4

/-- A successor pre-limit is a value that doesn't cover any other.

It's so named because in a successor order, a successor pre-limit can't be the successor of anything
smaller.

Use `IsSuccLimit` if you want to exclude the case of a minimal element. -/
def IsSuccPrelimit (a : α) : Prop :=
  ∀ b, ¬b ⋖ a

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