fact: Definition is_quotient_on (V : Open) (s : ∏ q : carrier U, localization_at (pr1 q)) : hProp := ∃ (f g : R), ∀ q : carrier U, V (pr1 q) ⇒ ∃ Hg : ¬ (pr1 q : prime_ideal R) g, s q = quotient f (g ,, Hg).
imports: UniMath.Algebra.RigsAndRings UniMath.Algebra.RigsAndRings.Ideals UniMath.MoreFoundations.AxiomOfChoice UniMath.MoreFoundations.Subtypes UniMath.Topology.Topology UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.Commring UniMath.AlgebraicGeometry.Topology UniMath.AlgebraicGeometry.SheavesOfRings