α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
dec_irr : (p : Associates α) → Decidable (Irreducible p)
inst✝ : UniqueFactorizationMonoid α
dec : DecidableEq α
dec' : DecidableEq (Associates α)
a b : Associates α
h : factors a = factors b
this : FactorSet.prod (factors a) = FactorSet.prod (factors b)
⊢ a = b
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
dec_irr : (p : Associates α) → Decidable (Irreducible p)
inst✝ : UniqueFactorizationMonoid α
dec : DecidableEq α
dec' : DecidableEq (Associates α)
a b : Associates α
h : factors a = factors b
⊢ a = b
have : a.factors.prod = b.factors.prod := by rw [h]
no goals
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
dec_irr : (p : Associates α) → Decidable (Irreducible p)
inst✝ : UniqueFactorizationMonoid α
dec : DecidableEq α
dec' : DecidableEq (Associates α)
a b : Associates α
h : factors a = factors b
this : FactorSet.prod (factors a) = FactorSet.prod (factors b)
⊢ a = b
rwa [factors_prod, factors_prod] at this
no goals
α : Type u_1
inst✝¹ : CancelCommMonoidWithZero α
dec_irr : (p : Associates α) → Decidable (Irreducible p)
inst✝ : UniqueFactorizationMonoid α
dec : DecidableEq α
dec' : DecidableEq (Associates α)
a b : Associates α
h : factors a = factors b
⊢ FactorSet.prod (factors a) = FactorSet.prod (factors b)
rw [h]