proposition: Lemma abses_reorder_pullback_pushout `{Univalence} {A A' B B' : AbGroup} (E : AbSES B A) (f : A $-> A') (g : B' $-> B) : abses_pushout f (abses_pullback g E) = abses_pullback g (abses_pushout f E).
proof: Proof. pose (F := absesmorphism_compose (abses_pushout_morphism E f) (abses_pullback_morphism E g)). refine (abses_pushout_is_pullback (Build_AbSESMorphism f (component2 F) g _ _)); apply F. Defined.
imports: Basics Types WildCat Pointed.Core AbGroups.AbelianGroup AbGroups.Biproduct AbGroups.AbHom AbSES.Core AbSES.Pullback AbSES.Pushout AbSES.DirectSum Homotopy.HSpace.Core