cases h with | intro a ha =>
simp only [map]
cases ha.left with
| head => rw [ha.right]; constructor
| tail x h' =>
  have h_in_tail := ih.mpr (Exists.intro a ⟨h', ha.right⟩)
  exact Mem.tail _ h_in_tail
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)
no goals