∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (s : Submodule R A)
  (h1 : 1 ∈ s) (hmul : ∀ (x y : A), x ∈ s → y ∈ s → x * y ∈ s),
  s.toSubalgebra h1 hmul =
    { carrier := ↑s, mul_mem' := hmul, one_mem' := h1, add_mem' := ⋯, zero_mem' := ⋯, algebraMap_mem' := ⋯ }