no goals
α : Type u_1
inst✝ : CancelCommMonoidWithZero α
p a : α
hp : Prime p
x✝ : Finite p a
⊢ ¬p ^ (0 + 1) ∣ a ^ 0
simp [mt isUnit_iff_dvd_one.2 hp.2.1]
α : Type u_1
inst✝ : CancelCommMonoidWithZero α
p a : α
hp : Prime p
k : ℕ
ha : Finite p a
⊢ Finite p (a * a ^ k)
α : Type u_1
inst✝ : CancelCommMonoidWithZero α
p a : α
hp : Prime p
k : ℕ
ha : Finite p a
⊢ Finite p (a ^ (k + 1))
rw [_root_.pow_succ]
no goals
α : Type u_1
inst✝ : CancelCommMonoidWithZero α
p a : α
hp : Prime p
k : ℕ
ha : Finite p a
⊢ Finite p (a * a ^ k)
exact finite_mul hp ha (finite_pow hp ha)