induction s with
| nil =>  
  simp [mulMonom, coords]
| cons h t ih => 
  simp [mulMonom, coords, monom_coords_at_zero]
  assumption
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
g x₀ : G
s : FormalSum R G
⊢ coords (mulMonom 0 g s) x₀ = 0
no goals