∀ {β : Type u_2} {α : Type u_1} [inst : LE β] [inst_1 : DecidableLE β] {f : α → β} {b : β}
  (motive : (xs : List α) → (h : xs ≠ []) → f (List.minOn f xs h) ≤ b → Prop) (xs : List α) (h : xs ≠ [])
  (h_1 : f (List.minOn f xs h) ≤ b),
  (∀ (x : α) (xs : List α) (h : x :: xs ≠ []) (h_2 : f (List.minOn f (x :: xs) h) ≤ b), motive (x :: xs) h h_2) →
    motive xs h h_1