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