abses_pushout_pcompose' `{Univalence} {A0 A1 A2 B : AbGroup} (f : A0 $-> A1) (g : A1 $-> A2) : abses_pushout' (B:=B) (g $o f) $=>* abses_pushout' g $o* abses_pushout' f. Proof. exists (abses_pushout_compose' f g). apply gpd_moveL_Vh. rapply Quotient_ind_hprop; intros [a2 [a0 b]]; simpl. by rewrite 7 grp_unit_l, 2 grp_unit_r. Defined.
Require Import Basics Types Truncations.Core. Require Import WildCat Pointed.Core Homotopy.ExactSequence HIT.epi. Require Import Modalities.ReflectiveSubuniverse. Require Import AbelianGroup AbPushout AbHom AbGroups.Biproduct. Require Import AbSES.Core AbSES.DirectSum.