simp only [List.map_eq_map_iff] at h2
v u : VarName
X : DefName
xs : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 :
  List.map (fun v => decide (v ∈ binders)) xs =
    List.map ((fun v => decide (v ∈ binders)) ∘ fun x => if v = x then u else x) xs
⊢ v ∈ xs → u ∉ binders
v u : VarName
X : DefName
xs : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : ∀ x ∈ xs, decide (x ∈ binders) = ((fun v => decide (v ∈ binders)) ∘ fun x => if v = x then u else x) x
⊢ v ∈ xs → u ∉ binders