simp [add_assoc]
case addCoeffs.h
R : Type
inst✝³ : Ring R
inst✝² : DecidableEq R
G : Type
inst✝¹ : Group G
inst✝ : DecidableEq G
s₁ s₂ : FormalSum R G
head' : R × G
tail' : List (R × G)
b : R
h : G
a₁ a₂ : R
x : G
tail : FormalSum R G
x₀ : G
rel' : ElementaryMove R G ((a₁, x) :: (a₂, x) :: tail) ((a₁ + a₂, x) :: tail) := addCoeffs a₁ a₂ x tail
prev : mul ((a₁, x) :: (a₂, x) :: tail) tail' ≈ mul ((a₁ + a₂, x) :: tail) tail' :=
  first_arg_invariant ((a₁, x) :: (a₂, x) :: tail) ((a₁ + a₂, x) :: tail) tail' rel'
pl : coords (mul ((a₁, x) :: (a₂, x) :: tail) tail') x₀ = coords (mul ((a₁ + a₂, x) :: tail) tail') x₀ :=
  congrFun prev x₀
⊢ monomCoeff R G x₀ (a₁ * b, x * h) + (monomCoeff R G x₀ (a₂ * b, x * h) + coords (mulMonom b h tail) x₀) +
      coords (mul ((a₁ + a₂, x) :: tail) tail') x₀ =
    monomCoeff R G x₀ (a₁ * b, x * h) + monomCoeff R G x₀ (a₂ * b, x * h) + coords (mulMonom b h tail) x₀ +
      coords (mul ((a₁ + a₂, x) :: tail) tail') x₀
no goals