Lemma type_iso_is_equiv (A B : ob type_precat) (f : iso A B) : isweq (pr1 f). Proof. apply (isweq_iso _ (inv_from_iso f)). - intro x. set (T:=iso_inv_after_iso f). set (T':=toforallpaths _ _ _ T). apply T'. - intro x. apply (toforallpaths _ _ _ (iso_after_iso_inv f)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Categories.Type.Core.