n p : ℕ
pp : Prime p
k x : ℕ
⊢ (∃ k_1, k_1 ≤ k ∧ x = p ^ k_1) ↔ ∃ j x_1, x = p ^ j
n p : ℕ
pp : Prime p
k x : ℕ
⊢ x ∈ divisors (p ^ k) ↔ ∃ j x_1, x = p ^ j
rw [mem_divisors, Nat.dvd_prime_pow pp, and_iff_left (ne_of_gt (pow_pos pp.pos k))]
no goals
n p : ℕ
pp : Prime p
k x : ℕ
⊢ (∃ k_1, k_1 ≤ k ∧ x = p ^ k_1) ↔ ∃ j x_1, x = p ^ j
simp