proposition: Lemma section_subset {H : V ⊆ U} {s t : section U} : restriction_section H s = restriction_section H t -> ∏ p : carrier U, V (pr1 p) -> s p = t p.
proof: Proof. intros Heq p HVp. apply (@pathscomp0 _ _ (restriction_section H s (pr1 p ,, HVp))). - apply pathsinv0, restriction_paths. - apply (@pathscomp0 _ _ (restriction_section H t (pr1 p ,, HVp))). + induction Heq. apply idpath. + apply restriction_paths. 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