∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
  [inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (l l_1 : A₁ ≃ₗ[R] A₂) (e_l : l = l_1) (map_one : l 1 = 1)
  (map_mul : ∀ (x y : A₁), l (x * y) = l x * l y),
  AlgEquiv.ofLinearEquiv l map_one map_mul = AlgEquiv.ofLinearEquiv l_1 ⋯ ⋯