induction xs
α β : Type
inst✝ : DecidableEq α
f g : α → β
xs : List α
x : α
h1 : x ∈ xs
⊢ updateListITE f xs (List.map g xs) x = g x
case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : x ∈ []
⊢ updateListITE f [] (List.map g []) x = g x

case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
x head✝ : α
tail✝ : List α
tail_ih✝ : x ∈ tail✝ → updateListITE f tail✝ (List.map g tail✝) x = g x
h1 : x ∈ head✝ :: tail✝
⊢ updateListITE f (head✝ :: tail✝) (List.map g (head✝ :: tail✝)) x = g x