intro h
case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
⊢ (∃ a, a ∈ x :: xs ∧ f a = b) → b ∈ map f (x :: xs)
case mpr
α : Type u_1
β : Type u_2
f : α → β
b : β
x : α
xs : List α
ih : b ∈ map f xs ↔ ∃ a, a ∈ xs ∧ f a = b
h : ∃ a, a ∈ x :: xs ∧ f a = b
⊢ b ∈ map f (x :: xs)