proposition: Lemma ap_abses_pullback `{Univalence} {A B B' : AbGroup} (f : B' $-> B) {E F : AbSES B A} (p : E = F) : ap (abses_pullback f) p = equiv_path_abses_iso (fmap (abses_pullback f) (equiv_path_abses_iso^-1 p)).
proof: Proof. induction p. nrefine (_ @ ap equiv_path_abses_iso _). 2: refine ((fmap_id_strong _ _)^ @ ap _ equiv_path_absesV_1^). exact equiv_path_abses_1^. Defined.
imports: Basics Types HSet Limits.Pullback WildCat Pointed.Core Homotopy.ExactSequence Modalities.ReflectiveSubuniverse AbGroups.AbelianGroup AbGroups.AbPullback AbGroups.Biproduct AbSES.Core AbSES.DirectSum