. intro ⟨h₁, h₂⟩ a ha;
  cases ha <;> simp_all;
case mpr
α : Type u_2
inst✝³ : LogicalConnective α
inst✝² : DecidableEq α
F : Type u_1
inst✝¹ : FunLike F α Prop
inst✝ : LogicalConnective.HomClass F α Prop
f : F
s₁ s₂ : Finset α
⊢ ((∀ a ∈ s₁, f a) ∧ ∀ a ∈ s₂, f a) → ∀ (a : α), a ∈ s₁ ∨ a ∈ s₂ → f a
no goals