apply Iff.intro
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 ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
case mp
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 ++ x :: (as ++ [y]) → z ∈ cs ++ y :: x :: as

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])