∀ {M : Type u_2} {N : Type u_1} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] [inst_2 : AddMonoid P]
  (x : AddMonoid.Coprod M N →+ P),
  AddMonoid.Coprod.lift (x.comp AddMonoid.Coprod.inl, x.comp AddMonoid.Coprod.inr).1
      (x.comp AddMonoid.Coprod.inl, x.comp AddMonoid.Coprod.inr).2 =
    x