Definition nat_iso_inv_trans {C D : precategory} {F G : C ⟶ D} (μ : nat_iso F G) : G ⟹ F. Proof. use make_nat_trans. - exact (λ x, inv_from_iso (make_iso _ (pr2 μ x))). - abstract (intros x y f ; cbn ; refine (!_) ; use iso_inv_on_right ; cbn ; rewrite !assoc ; use iso_inv_on_left ; cbn ; exact (!(nat_trans_ax (pr1 μ) _ _ f))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence.