rewrite [Permutation.sign_cyclic_cons]
m n : Nat
i : Fin m
j : Fin n
⊢ Permutation.sign
      (Permutation.cyclic
        (Fin.restrict (Board.pivot i j) (_ : ↑(Board.pivot i j) < (m + 1) * (n + 1) - 1) ::
          List.pmap Fin.restrict (Board.path i j)
            (_ : ∀ (a : Fin ((m + 1) * (n + 1))), a ∈ Board.path i j → ↑a < (m + 1) * (n + 1) - 1))) =
    false
m n : Nat
i : Fin m
j : Fin n
⊢ (List.length
          (List.pmap Fin.restrict (Board.path i j)
            (_ : ∀ (a : Fin ((m + 1) * (n + 1))), a ∈ Board.path i j → ↑a < (m + 1) * (n + 1) - 1)) %
        2 ==
      1) =
    false

m n : Nat
i : Fin m
j : Fin n
⊢ ¬Fin.restrict (Board.pivot i j) (_ : ↑(Board.pivot i j) < (m + 1) * (n + 1) - 1) ∈
      List.pmap Fin.restrict (Board.path i j)
        (_ : ∀ (a : Fin ((m + 1) * (n + 1))), a ∈ Board.path i j → ↑a < (m + 1) * (n + 1) - 1)