α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b : α
h : lcm a b = 0
this : Associated (a * b) 0
⊢ a = 0 ∨ b = 0
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b : α
h : lcm a b = 0
⊢ a = 0 ∨ b = 0
have : Associated (a * b) 0 := (gcd_mul_lcm a b).symm.trans <| by rw [h, mul_zero]
no goals
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b : α
h : lcm a b = 0
this : Associated (a * b) 0
⊢ a = 0 ∨ b = 0
rwa [← mul_eq_zero, ← associated_zero_iff_eq_zero]
no goals
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b : α
h : lcm a b = 0
⊢ Associated (gcd a b * lcm a b) 0
rw [h, mul_zero]
no goals
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
inst✝ : GCDMonoid α
a b : α
⊢ a = 0 ∨ b = 0 → lcm a b = 0
rintro (rfl | rfl) <;> [apply lcm_zero_left; apply lcm_zero_right]