prelimitRecOn_of_isSuccPrelimit — Mathlib

English

If b is succ-prelimit, then the limitRecOn reduces to isSuccPrelimit on b.

Русский

Если b имеет succ-предпределение, предел-рекурсии сводится к isSuccPrelimit на b.

LaTeX

$$$\\mathrm{isSuccLimitRecOn}(b, isMin, succ, isSuccLimit) = \\mathrm{isSuccPrelimit}(b, hb) \\; (\\ldots)$ where $hb$ encodes pred limits.$$

Lean4

@[simp]
theorem prelimitRecOn_of_isSuccPrelimit (hb : IsSuccPrelimit b) :
    prelimitRecOn b succ isSuccPrelimit = isSuccPrelimit b hb fun x _ ↦ SuccOrder.prelimitRecOn x succ isSuccPrelimit :=
  by rw [prelimitRecOn, WellFounded.fix_eq, dif_pos hb]; rfl

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