intros
case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
⊢ ∀ (acc : List κ),
    k ∈ acc → length (uniqueAux (map Prod.fst []) acc) = length (uniqueAux (map Prod.fst (matchKey [] k).snd) acc)
case nil
κ : Type u_1
ν : Type u_2
inst✝ : DecidableEq κ
k : κ
acc✝ : List κ
hk✝ : k ∈ acc✝
⊢ length (uniqueAux (map Prod.fst []) acc✝) = length (uniqueAux (map Prod.fst (matchKey [] k).snd) acc✝)