simp_rw [add_mul, AddMonoidAlgebra.single_add, sum_add]
case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
n : ℕ
r1 r2 : R
⊢ (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) ((r1 + r2) * (↑φ)^[n] b₂)) =
    (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r1 * (↑φ)^[n] b₂)) +
      sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r2 * (↑φ)^[n] b₂)
no goals