induction s₁ with
| nil =>
  simp [coords]
| cons h t ih =>
  simp [coords, ← ih, add_assoc]
R : Type u_1
inst✝² : Ring R
inst✝¹ : DecidableEq R
X : Type u_2
inst✝ : DecidableEq X
s₁ s₂ : FormalSum R X
x₀ : X
⊢ coords s₁ x₀ + coords s₂ x₀ = coords (s₁ ++ s₂) x₀
no goals