rw [ps]
case cons.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
a : R
x : G
s₁ s₂ : FormalSum R G
r : ElementaryMove R G s₁ s₂
a_ih✝ : mul s₁ ((b, h) :: tail') ≈ mul s₂ ((b, h) :: tail')
x₀ : G
rel' : ElementaryMove R G ((a, x) :: s₁) ((a, x) :: s₂) := cons a x s₁ s₂ r
prev : mul ((a, x) :: s₁) tail' ≈ mul ((a, x) :: s₂) tail' :=
  first_arg_invariant ((a, x) :: s₁) ((a, x) :: s₂) tail' rel'
pl : coords (mul ((a, x) :: s₁) tail') x₀ = coords (mul ((a, x) :: s₂) tail') x₀ := congrFun prev x₀
ps : coords (mulMonom b h s₁) x₀ = coords (mulMonom b h s₂) x₀ := mul_monom_invariant b h x₀ s₁ s₂ r
⊢ monomCoeff R G x₀ (a * b, x * h) + coords (mulMonom b h s₁) x₀ + coords (mul ((a, x) :: s₂) tail') x₀ =
    monomCoeff R G x₀ (a * b, x * h) + coords (mulMonom b h s₂) x₀ + coords (mul ((a, x) :: s₂) tail') x₀
no goals