∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] (F : CategoryTheory.Functor J AddCommGrpCat)
  (c : CategoryTheory.Limits.Cocone F) [inst_1 : DecidableEq J] (j : J) (x : ↑(F.obj j)),
  (AddCommGrpCat.Colimits.Quot.desc F c) ((AddCommGrpCat.Colimits.Quot.ι F j) x) =
    (CategoryTheory.ConcreteCategory.hom (c.ι.app j)) x