induction s with
| nil =>
  simp [coords]
| cons h t ih =>
  simp [scmul, coords, monom_coords_mul, left_distrib, ih]
R : Type u_1
inst✝² : Ring R
inst✝¹ : DecidableEq R
X : Type u_2
inst✝ : DecidableEq X
r : R
s : FormalSum R X
x₀ : X
⊢ r * coords s x₀ = coords (scmul r s) x₀
no goals