isPredLimitRecOn — Mathlib

English

If b is not minimal, then isPredLimitRecOn(pred(b)) equals pred(b) hb.

Русский

Если b не минимален, then isPredLimitRecOn(pred(b)) = pred(b, hb).

LaTeX

$$$\\mathrm{isPredLimitRecOn}(\\mathrm{Order.pred}(b), isMax, pred, isPredLimit) = pred(b, hb)$ with hb: ¬IsMin(b).$$

Lean4

/-- A value can be built by building it on maximal elements, predecessors,
and predecessor limits. -/
@[elab_as_elim]
noncomputable def isPredLimitRecOn : motive b :=
  isSuccLimitRecOn (α := αᵒᵈ) b isMax pred (fun a ha => isPredLimit a ha.dual)

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