proposition: Lemma nat_trans_inv_pointwise_inv_after_z_iso (C : precategory_data) (C' : precategory) (hs: has_homsets C') (F G : ob [C, C', hs]) (A : F --> G) (Aiso: is_z_isomorphism A) : ∏ a : C, pr1 A a · pr1 (inv_from_z_iso (A,,Aiso)) a = identity _ .
proof: Proof. intro a. set (TA := z_iso_inv_after_z_iso (A,,Aiso)). apply (nat_trans_eq_pointwise TA). Qed.
imports: UniMath.Foundations.Propositions UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence