{F X Y : pType} {i : F ->* X} {f : X ->* Y} `{forall y y' : Y, In O (y = y')} `{MapIn O _ _ i} (ex : IsExact O i f) : i o pequiv_inverse (equiv_cxfib ex) == pfib _. Proof. rapply equiv_ind. 1: exact (isequiv_cxfib ex). intro x. exact (ap (fun g => i g) (eissect _ x)). Defined.
Require Import Basics Types. Require Import SuccessorStructure. Require Import WildCat. Require Import Pointed. Require Import Modalities.Identity Modalities.Descent. Require Import Truncations. Require Import HFiber. Require Import ObjectClassifier.