∀ {R : Type u_3} {P : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing P] [inst_2 : CommRing S]
  [inst_3 : Algebra R P] [inst_4 : Algebra P S] (l : TensorProduct P S Ω[P⁄R] →ₗ[P] ↥(RingHom.ker (algebraMap P S))),
  l ∘ₗ KaehlerDifferential.kerToTensor R P S = LinearMap.id →
    ∀ (σ : S → P),
      (∀ (x : S), (algebraMap P S) (σ x) = x) →
        ∀ (a b : S),
          σ (a + b) - ↑(l (1 ⊗ₜ[P] (KaehlerDifferential.D R P) (σ (a + b)))) =
            σ a - ↑(l (1 ⊗ₜ[P] (KaehlerDifferential.D R P) (σ a))) +
              (σ b - ↑(l (1 ⊗ₜ[P] (KaehlerDifferential.D R P) (σ b))))