conv =>
  lhs; rewrite [Nat.not_beq_eq_true_eq]
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
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 ↔ (Nat.succ (List.length l) % 2 == 1) = true