{G H : ZeroGpd} (f : G $<~> H) (x : H) (y : G) (p : equiv_fun_0gpd f y $== x) : y $== equiv_fun_0gpd f^-1$ x := (cat_eissect f y)^$ $@ fmap (equiv_fun_0gpd f^-1$) p. Global Instance issurjinj_equiv_0gpd {G H : ZeroGpd} (f : G $<~> H) : IsSurjInj (equiv_fun_0gpd f). Proof. econstructor. - intro y. exists (equiv_fun_0gpd f^-1$ y). rapply cat_eisretr. - apply isinj_equiv_0gpd. Defined.
Require Import Basics.Overture Basics.Tactics Require Import WildCat.Core WildCat.Equiv WildCat.EquivGpd