∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] (s : S) (motive : (∃ x, s * (algebraMap R S) ↑x.2 = (algebraMap R S) x.1) → Prop)
  (x : ∃ x, s * (algebraMap R S) ↑x.2 = (algebraMap R S) x.1),
  (∀ (x y : R) (hy : y ∈ M) (H : s * (algebraMap R S) ↑(x, ⟨y, hy⟩).2 = (algebraMap R S) (x, ⟨y, hy⟩).1), motive ⋯) →
    motive x