Lemma nat_trans_inv_pointwise_inv_before (C : precategory_data) (C' : precategory) (hs: has_homsets C') (F G : ob [C, C', hs]) (A : F --> G) (Aiso: is_iso A) : ∏ a : C, pr1 (inv_from_iso (make_iso A Aiso)) a · pr1 A a = identity _ . Proof. intro a. set (TA' := iso_after_iso_inv (make_iso A Aiso)). apply (nat_trans_eq_pointwise TA'). Qed.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.