{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] →
                let P' := P ⧸ RingHom.ker (algebraMap P S) ^ 2;
                (motive : { l // l ∘ₗ KaehlerDifferential.kerToTensor R P' S = LinearMap.id } → Sort u_4) →
                  (x : { l // l ∘ₗ KaehlerDifferential.kerToTensor R P' S = LinearMap.id }) →
                    ((l : TensorProduct P' S Ω[P'⁄R] →ₗ[P'] ↥(RingHom.ker (algebraMap P' S))) →
                        (hl : l ∘ₗ KaehlerDifferential.kerToTensor R P' S = LinearMap.id) → motive ⟨l, hl⟩) →
                      motive x