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