∀ {R : Type u_3} {S : Type u_4} {ι : Type u_1} {σ : Type u_2} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (i : ι),
  (¬∀ (i_1 : σ), (if i = P.map i_1 then 1 else 0) = 0) → i ∈ Set.range P.map