rewrite [List.mem_cons, not_or] at hk
case cons.cons
m n : Nat
f : Fin n → Fin n
f_inj : ∀ (i j : Fin n), f i = f j → i = j
j k k' : Fin n
l : List (Fin n)
hk : ¬k ∈ k' :: l
hfk : f k = f k' ∨ f k ∈ k' :: l
hfk' : ¬f k' ∈ k' :: l
htail : OrbitChain f k' l j
IH : f k ∈ k' :: l → f k = j
⊢ f k = j
case cons.cons
m n : Nat
f : Fin n → Fin n
f_inj : ∀ (i j : Fin n), f i = f j → i = j
j k k' : Fin n
l : List (Fin n)
hk : ¬k = k' ∧ ¬k ∈ l
hfk : f k = f k' ∨ f k ∈ k' :: l
hfk' : ¬f k' ∈ k' :: l
htail : OrbitChain f k' l j
IH : f k ∈ k' :: l → f k = j
⊢ f k = j