rw [← append_coords]
case cons
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
x₀ : G
s₁ s₃ : FormalSum R G
head : R × G
tail : List (R × G)
ih : coords (mul s₁ (tail ++ s₃)) x₀ = coords (mul s₁ tail) x₀ + coords (mul s₁ s₃) x₀
⊢ coords (mulMonom head.1 head.2 s₁ ++ mul s₁ (tail ++ s₃)) x₀ =
    coords (mulMonom head.1 head.2 s₁ ++ mul s₁ tail) x₀ + coords (mul s₁ s₃) x₀
case cons
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
x₀ : G
s₁ s₃ : FormalSum R G
head : R × G
tail : List (R × G)
ih : coords (mul s₁ (tail ++ s₃)) x₀ = coords (mul s₁ tail) x₀ + coords (mul s₁ s₃) x₀
⊢ coords (mulMonom head.1 head.2 s₁) x₀ + coords (mul s₁ (tail ++ s₃)) x₀ =
    coords (mulMonom head.1 head.2 s₁ ++ mul s₁ tail) x₀ + coords (mul s₁ s₃) x₀