{R : Type u_1} →
  {P : Type u_2} →
    {S : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : CommRing P] →
          [inst_2 : CommRing S] →
            [inst_3 : Algebra R P] →
              [inst_4 : Algebra P S] →
                [inst_5 : Algebra R S] →
                  [inst_6 : IsScalarTower R P S] →
                    (g : S →ₐ[R] P) →
                      RingHom.ker (algebraMap P S) ^ 2 = ⊥ →
                        (IsScalarTower.toAlgHom R P S).comp g = AlgHom.id R S →
                          TensorProduct P S Ω[P⁄R] →ₗ[P] ↥(RingHom.ker (algebraMap P S))