m n : ℕ+
⊢ ↑m ∣ ↑n ↔ gcd m n = m
m n : ℕ+
⊢ m ∣ n ↔ gcd m n = m
rw [dvd_iff]
m n : ℕ+
⊢ Nat.gcd ↑m ↑n = ↑m ↔ gcd m n = m
m n : ℕ+
⊢ ↑m ∣ ↑n ↔ gcd m n = m
rw [Nat.gcd_eq_left_iff_dvd]
m n : ℕ+
⊢ Nat.gcd ↑m ↑n = ↑m ↔ ↑(gcd m n) = ↑m
m n : ℕ+
⊢ Nat.gcd ↑m ↑n = ↑m ↔ gcd m n = m
rw [← coe_inj]
no goals
m n : ℕ+
⊢ Nat.gcd ↑m ↑n = ↑m ↔ ↑(gcd m n) = ↑m
simp