proposition: Lemma gluing_structure_presheaf (ac : AxiomOfChoice) : gluing structure_presheaf.
proof: Proof. intros A g Hg. set (H0 := ac (carrier_subset (⋃ A)) _ (@hexists_open_neighborhood _ A)). use (hinhfun _ H0); intro H. exists (glue_sections g Hg H). intro U. apply funext_section. intro q. induction q as [q HUq]. cbn. apply section_intersection, Hg. Qed.
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