intros A f n
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ∀ {A : Sort u_1} (f : A → A) (n : ℕ) (x : A), f^[n + 1] x = f (f^[n] x)
A✝ : Type
R : A✝ → A✝ → Prop
inhabited_A : Nonempty A✝
A : Sort u_1
f : A → A
n : ℕ
⊢ ∀ (x : A), f^[n + 1] x = f (f^[n] x)