no goals
α : Type u_1
β : Type u_2
γ : Type ?u.43806
ι : Sort u_3
f✝ f₁ f₂ : Filter α
h h₁ h₂ : Set α → Set β
f : ι → Filter α
g : Set α → Set β
hg : ∀ {s t : Set α}, g (s ∩ t) = g s ∩ g t
hg' : g univ = univ
s t : Set α
⊢ (𝓟 ∘ g) (s ∩ t) = (𝓟 ∘ g) s ⊓ (𝓟 ∘ g) t
simp only [inf_principal, comp, hg]
no goals
α : Type u_1
β : Type u_2
γ : Type ?u.43806
ι : Sort u_3
f✝ f₁ f₂ : Filter α
h h₁ h₂ : Set α → Set β
f : ι → Filter α
g : Set α → Set β
hg : ∀ {s t : Set α}, g (s ∩ t) = g s ∩ g t
hg' : g univ = univ
⊢ (𝓟 ∘ g) univ = ⊤
rw [Function.comp_apply, hg', principal_univ]