intro x₁ x₂
case refine_2.f_inj
α : Type u
β : Type v
inst✝³ : BishopFin α
inst✝² : BishopFin β
p q : α → Prop
inst✝¹ : DecidablePred p
inst✝ : DecidablePred q
⊢ ∀ (a₁ a₂ : { a // ¬(q ∘ Subtype.val) a }),
    { val := a₁.val.val, property := (_ : p a₁.val.val ∧ ¬q a₁.val.val) } =
        { val := a₂.val.val, property := (_ : p a₂.val.val ∧ ¬q a₂.val.val) } →
      a₁ = a₂
case refine_2.f_inj
α : Type u
β : Type v
inst✝³ : BishopFin α
inst✝² : BishopFin β
p q : α → Prop
inst✝¹ : DecidablePred p
inst✝ : DecidablePred q
x₁ x₂ : { a // ¬(q ∘ Subtype.val) a }
⊢ { val := x₁.val.val, property := (_ : p x₁.val.val ∧ ¬q x₁.val.val) } =
      { val := x₂.val.val, property := (_ : p x₂.val.val ∧ ¬q x₂.val.val) } →
    x₁ = x₂