∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  (map_one : LinearMap.id 1 = 1) (map_mul : ∀ (x y : A), LinearMap.id (x * y) = LinearMap.id x * LinearMap.id y),
  AlgHom.ofLinearMap LinearMap.id map_one map_mul = AlgHom.id R A