∀ (G : Type u_1) [inst : AddCommGroup G] (p : ℕ) [hp : Fact (Nat.Prime p)] {g : G}
  (motive : g ∈ (AddCommMonoid.primaryComponent G p).carrier → Prop)
  (x : g ∈ (AddCommMonoid.primaryComponent G p).carrier), (∀ (n : ℕ) (hn : addOrderOf g = p ^ n), motive ⋯) → motive x