F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
⊢ ∀ (a : List α), traverse h (map g (Quotient.mk (isSetoid α) a)) = traverse (h ∘ g) (Quotient.mk (isSetoid α) a)
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
⊢ traverse h (map g x) = traverse (h ∘ g) x
refine' Quotient.inductionOn x _
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
a✝ : List α
⊢ traverse h (map g (Quotient.mk (isSetoid α) a✝)) = traverse (h ∘ g) (Quotient.mk (isSetoid α) a✝)
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
⊢ ∀ (a : List α), traverse h (map g (Quotient.mk (isSetoid α) a)) = traverse (h ∘ g) (Quotient.mk (isSetoid α) a)
intro
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
a✝ : List α
⊢ Coe.coe <$> Traversable.traverse h (List.map g a✝) = Coe.coe <$> Traversable.traverse (h ∘ g) a✝
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
a✝ : List α
⊢ traverse h (map g (Quotient.mk (isSetoid α) a✝)) = traverse (h ∘ g) (Quotient.mk (isSetoid α) a✝)
simp only [traverse, quot_mk_to_coe, coe_map, lift_coe, Function.comp_apply]
no goals
F : Type u → Type u
inst✝³ : Applicative F
inst✝² : CommApplicative F
α' β' : Type u
f : α' → F β'
G : Type u_1 → Type u_1
inst✝¹ : Applicative G
inst✝ : CommApplicative G
α β γ : Type u_1
g : α → β
h : β → G γ
x : Multiset α
a✝ : List α
⊢ Coe.coe <$> Traversable.traverse h (List.map g a✝) = Coe.coe <$> Traversable.traverse (h ∘ g) a✝
rw [← Traversable.traverse_map h g, List.map_eq_map]