∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] (f : R →* S) (p : ℕ)
  [inst_2 : ExpChar R p] [inst_3 : ExpChar S p] (x : R), (frobenius S p) (f x) = f ((frobenius R p) x)