proposition: Lemma z_iso_from_is_relmonadmor_z_iso_idtoiso {C : precategory_data} (D : category) (J : functor C D) {R R': RelMonad J} (p : @paths (category_RelMonad D J) R R'): z_iso_from_is_relmonadmor_z_iso D J (idtoiso p) = idtoiso(C := [C, D]) (maponpaths (@R_functor C D J) p).
proof: Proof. unfold z_iso_from_is_relmonadmor_z_iso. simpl. apply (z_iso_eq(C := [C, D])). simpl. apply (nat_trans_eq D). intro c. induction p. apply idpath. 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