Lemma eqweq_maponpaths_mor {A B : precategory} (F G : A ≃ B) (p : F = G) (a a' : A) (f : F a --> F a') : eqweqmap (maponpaths (λ T : A ≃ B, (pr1 T) a --> (pr1 T) a') p) f = (idtomor _ _ (!toforallpaths _ _ _ (maponpaths pr1 p) a)) · f · (idtomor _ _ (toforallpaths _ _ _ (maponpaths pr1 p) a')). Proof. induction p. rewrite id_left. rewrite id_right. reflexivity. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful.