induction xs
α β : Type
inst✝ : DecidableEq α
xs : List α
f : α → β
a : α
b : β
h1 : a ∉ xs
⊢ List.map (updateITE f a b) xs = List.map f xs
case nil
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
b : β
h1 : a ∉ []
⊢ List.map (updateITE f a b) [] = List.map f []

case cons
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
b : β
head✝ : α
tail✝ : List α
tail_ih✝ : a ∉ tail✝ → List.map (updateITE f a b) tail✝ = List.map f tail✝
h1 : a ∉ head✝ :: tail✝
⊢ List.map (updateITE f a b) (head✝ :: tail✝) = List.map f (head✝ :: tail✝)