theorem extracted_formal_statement_8 {m : ℕ+} (x y : EuclideanSpace ℝ (Fin ↑m)) :
  ∑ x_1, y x_1 * x x_1 = ∑ i, x i * y i := sorry

State before:
m : ℕ+
x y : EuclideanSpace ℝ (Fin ↑m)
⊢ ∑ x_1, y x_1 * x x_1 = ∑ i, x i * y i

Tactic: simp [mul_comm]

State after:

Relevant lemmas:
mul_comm : ∀ {G : Type u_1} [inst : CommMagma G] (a b : G), a * b = b * a