rw [Function.surjInv_eq
      (pth_power_bijective_of_char_nonzero (by assumption)).surjective,
    zero_pow]
case inr
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : PerfectRing R
h✝ : ¬ringChar R = 0
⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 ^ ringChar R = 0 ^ ringChar R
case inr
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : PerfectRing R
h✝ : ¬ringChar R = 0
⊢ 0 < ringChar R