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

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