∀ {P : {R S : Type u_1} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop} (S : Type u_1) ⦃T : Type u_1⦄
  [inst : CommRing S] [inst_1 : CommRing T] (f : S →+* T)
  (motive : RingHom.Locally (fun {R S} [CommRing R] [CommRing S] => P) f → Prop)
  (h : RingHom.Locally (fun {R S} [CommRing R] [CommRing S] => P) f),
  (∀ (s : Set T) (hsone : Ideal.span s = ⊤)
      (hs : ∀ t ∈ s, (fun {R S} [CommRing R] [CommRing S] => P) ((algebraMap T (Localization.Away t)).comp f)),
      motive ⋯) →
    motive h