rfl
n : Nat
x : Permutation n
i j : Fin n
k : Nat
hk : k < n
⊢ (if ↑j = k then x.val[↑i] else if ↑i = k then x.val[↑j] else x.val[k]) =
    if ↑j = k then x[↑i] else if ↑i = k then x[↑j] else x[k]
no goals