rewrite [sign_swap _ i j h.1, IH h.2, Bool.eq_iff_iff]
case cons
m n✝ n : Nat
i j : Fin n
l : List (Fin n)
IH : ¬i ∈ l → sign (List.foldr (fun j x => swap x i j) 1 l) = (List.length l % 2 == 1)
h : ¬i = j ∧ ¬i ∈ l
⊢ sign (swap (List.foldr (fun j x => swap x i j) 1 l) i j) = (Nat.succ (List.length l) % 2 == 1)
case cons
m n✝ n : Nat
i j : Fin n
l : List (Fin n)
IH : ¬i ∈ l → sign (List.foldr (fun j x => swap x i j) 1 l) = (List.length l % 2 == 1)
h : ¬i = j ∧ ¬i ∈ l
⊢ (!List.length l % 2 == 1) = true ↔ (Nat.succ (List.length l) % 2 == 1) = true