case nil =>
  simp at h1
  simp only [Function.updateListITE]
  exact h2
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v
no goals