Lemma opp_is_inverse_in_precat {C : precategory} {a b : C} {f : a --> b} {g : b --> a} : @is_inverse_in_precat C a b f g -> @is_inverse_in_precat (opp_precat C) a b g f. Proof. intros H. use make_is_inverse_in_precat. - exact (is_inverse_in_precat1 H). - exact (is_inverse_in_precat2 H). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.FunctorCategory.