∀ {R₁ : Type u_1} {M₁ : Type u_2} [inst : CommSemiring R₁] [inst_1 : AddCommMonoid M₁] [inst_2 : Module R₁ M₁]
  {n : Type u_5} [inst_3 : Fintype n] [inst_4 : DecidableEq n] (b : Module.Basis n R₁ M₁)
  (B : LinearMap.BilinForm R₁ M₁) (M : Matrix n n R₁),
  M * (LinearMap.BilinForm.toMatrix b) B =
    (LinearMap.BilinForm.toMatrix b) (B.compLeft ((Matrix.toLin b b) M.transpose))