induction s with
| nil => 
  simp [mulMonom, coords]
| cons head tail ih =>
  let (a₁, x₁) := head
  simp [mulMonom, coords, mul_assoc]
  rw [ih]
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
x : G
a b : R
h x₀ : G
s : FormalSum R G
⊢ coords (mulMonom b h (mulMonom a x s)) x₀ = coords (mulMonom (a * b) (x * h) s) x₀
no goals