simp only [if_neg hjk, if_neg hik]
n : Nat
x : Permutation n
i j : Fin n
k : Nat
hk : k < n
hjk : ¬↑j = k
hik : ¬↑i = k
⊢ x[↑(if ↑j = k then i else if ↑i = k then j else { val := k, isLt := hk })] =
    if ↑j = k then x[↑i] else if ↑i = k then x[↑j] else x[k]
no goals