. exact nodup_elems.map f f_inj
case refine_1
α : Type u
β : Type v
inst✝¹ : BishopFin α
inst✝ : BishopFin β
f : α → β
f_inj : ∀ (a₁ a₂ : α), f a₁ = f a₂ → a₁ = a₂
⊢ List.Nodup (List.map f (elems α))

case refine_2
α : Type u
β : Type v
inst✝¹ : BishopFin α
inst✝ : BishopFin β
f : α → β
f_inj : ∀ (a₁ a₂ : α), f a₁ = f a₂ → a₁ = a₂
⊢ List.map f (elems α) ⊆ elems β
case refine_2
α : Type u
β : Type v
inst✝¹ : BishopFin α
inst✝ : BishopFin β
f : α → β
f_inj : ∀ (a₁ a₂ : α), f a₁ = f a₂ → a₁ = a₂
⊢ List.map f (elems α) ⊆ elems β