∀ {R : Type u_4} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  [inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] {P : Algebra.Extension R S}
  {Q : Algebra.Extension R T} (f : P.Hom Q) [alg : Algebra P.Ring Q.Ring]
  (halg : algebraMap P.Ring Q.Ring = f.toRingHom),
  f.toRingHom.FormallyEtale →
    ∀ (H₂ : Function.Bijective ⇑(LinearMap.liftBaseChange Q.Ring (f.mapKer halg))) (x : Q.H1Cotangent),
      (LinearMap.baseChange T P.cotangentComplex) ((Algebra.Extension.tensorCotangent f halg H₂).symm ↑x) = 0