hfiber_cxfib'_induced_path' `{Univalence} {A B C : AbGroup} (E : AbSES C B) (F : AbSES (middle E) A) (p : abses_pullback (inclusion E) F $== pt) (Y : hfiber_cxfib' E F p) : path_hfiber_cxfib' (hfiber_cxfib'_inhabited E F p) Y. Proof. exists (0 E F p Y). rapply gpd_moveR_Vh. rapply gpd_moveL_hM. rapply gpd_moveR_Vh. intro x. srapply equiv_path_pullback_hset; split. 2: exact (snd Y.2.1^$.2 x)^. reflexivity. Defined.
Require Import Basics Types HSet HFiber Limits.Pullback. Require Import WildCat Pointed.Core Homotopy.ExactSequence. Require Import Groups.QuotientGroup. Require Import AbGroups.AbelianGroup AbGroups.AbPullback AbGroups.Biproduct. Require Import AbSES.Core AbSES.Pullback. Require Import Modalities.Identity Modalities.Modality Truncations.Core.