`{Univalence} {A B C : AbGroup} (f : A $-> B) (g : A $-> C) (bc0 bc1 : ab_biprod B C) : @in_cosetL (ab_biprod B C) (ab_pushout_subgroup f g) bc0 bc1 <~> (grp_quotient_map bc0 = grp_quotient_map bc1 :> ab_pushout f g). Proof. rapply path_quotient. Defined.
Require Import Basics Types Truncations.Core. Require Import WildCat.Core HSet. Require Import AbGroups.AbelianGroup AbGroups.Biproduct.