∀ (R : Type u_1) (X : Type u_2) [inst : CommRing R] (x y z : FreeLieAlgebra R X),
  Quot.map₂ (fun x1 x2 => x1 * x2) ⋯ ⋯ x (y + z) =
    Quot.map₂ (fun x1 x2 => x1 * x2) ⋯ ⋯ x y + Quot.map₂ (fun x1 x2 => x1 * x2) ⋯ ⋯ x z