induction s₁ with
| nil => 
  simp [mulMonom, coords]
| cons head tail ih =>
  simp [mulMonom, coords]
  rw [ih]
  simp [add_assoc]
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
b : R
h x₀ : G
s₁ s₂ : FormalSum R G
⊢ coords (mulMonom b h (s₁ ++ s₂)) x₀ = coords (mulMonom b h s₁) x₀ + coords (mulMonom b h s₂) x₀
no goals