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 p : α
ha0 : a ≠ 0
hp : Irreducible p
hd : p ∣ a
⊢ Associates.mk p ∈ ↑(factors' a)
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 p : α
ha0 : a ≠ 0
hp : Irreducible p
hd : p ∣ a
⊢ Associates.mk p ∈ factors (Associates.mk a)
rw [factors_mk _ ha0]
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 p : α
ha0 : a ≠ 0
hp : Irreducible p
hd : p ∣ a
⊢ Associates.mk p ∈ ↑(factors' a)
exact mem_factorSet_some.mpr (mem_factors'_of_dvd ha0 hp hd)