have : (x :: xs).dedup s = x :: xs.dedup s := if_neg ha
α : Type u_1
s : Setoid α
inst✝ : DecidableRel Setoid.r
xs✝ : List α
x : α
xs : List α
ih : ∀ {i : xs.Index} {j : (List.dedup s xs).Index}, Setoid.r i.val j.val → dedup s i = j
i✝ : (x :: xs).Index
j : (List.dedup s (x :: xs)).Index
i : xs.Index
h : Setoid.r i.val j.val
ha : ¬Logic.Any (List.map (Setoid.r x) xs)
⊢ (let_fun this := ⋯;
    ⋯ ▸ (dedup s i).tail) =
    j
α : Type u_1
s : Setoid α
inst✝ : DecidableRel Setoid.r
xs✝ : List α
x : α
xs : List α
ih : ∀ {i : xs.Index} {j : (List.dedup s xs).Index}, Setoid.r i.val j.val → dedup s i = j
i✝ : (x :: xs).Index
j : (List.dedup s (x :: xs)).Index
i : xs.Index
h : Setoid.r i.val j.val
ha : ¬Logic.Any (List.map (Setoid.r x) xs)
this : List.dedup s (x :: xs) = x :: List.dedup s xs
⊢ (let_fun this := ⋯;
    ⋯ ▸ (dedup s i).tail) =
    j