proposition: Lemma is_functor_structure_presheaf_data : is_functor structure_presheaf_data.
proof: Proof. use make_dirprod. - intro U. apply rigfun_paths, funextsec. intro s. apply subtypePath_prop, idpath. - intros U V W f g. apply rigfun_paths, funextsec. intro s. apply subtypePath_prop, idpath. 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