proposition: Lemma pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso_idtoiso {C : precategory_data} {D : category} (H: is_univalent D) (J : functor C D) {R R': RelMonad J} (p: @paths (category_RelMonad D J) R R'): pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso H J (idtoiso p) = base_paths (pr1 R) (pr1 R') (base_paths R R' p).
proof: Proof. unfold pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso. simpl. rewrite (z_iso_from_is_relmonadmor_z_iso_idtoiso D J). rewrite functor_eq_from_functor_z_iso_idtoiso. apply pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso_idtoiso_aux. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core