. intros h
  cases mem_append_iff.mpr h with
  | inl hcs => exact List.mem_append_front _ _ _ hcs
  | inr hcons =>
    apply List.mem_append_back
    cases hcons with
    | head _ =>
      apply List.Mem.tail
      apply List.mem_append_back
      apply (List.mem_singleton_iff y y).mpr rfl
    | tail _ hcons' =>
      rw [←cons_append]
      exact List.mem_append_front _ _ _ hcons'
case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y])
no goals