simp only [get_mul, get_transpos, get_swap]
n : Nat
x : Permutation n
i j : Fin n
k : Nat
hk : k < n
⊢ (x * transpos i j)[k] = (swap x i j)[k]
n : Nat
x : Permutation n
i j : Fin n
k : Nat
hk : k < n
⊢ 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]