simp only [uniqueAux]
case cons
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
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length (uniqueAux (z :: zs) (cs ++ x :: (as ++ [y]))) = length (uniqueAux (z :: zs) (cs ++ y :: x :: as))
case cons
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
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length
      (if z ∈ cs ++ x :: (as ++ [y]) then uniqueAux zs (cs ++ x :: (as ++ [y]))
      else uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) =
    length
      (if z ∈ cs ++ y :: x :: as then uniqueAux zs (cs ++ y :: x :: as) else uniqueAux zs (z :: (cs ++ y :: x :: as)))