∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
  [inst_2 : AddMonoid X] [inst_3 : DistribMulAction R X] (r₁ : X) (s₁ : ↥S) (r₂ : X) (s₂ : ↥S) (rb sb : R),
  sb * ↑s₁ = rb * ↑s₂ → ∀ (h : sb * ↑s₁ ∈ S), OreLocalization.add''✝ r₁ s₁ r₂ s₂ = (sb • r₁ + rb • r₂) /ₒ ⟨sb * ↑s₁, h⟩