∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] (x y : N),
  AddMonoid.Coprod.mk (FreeAddMonoid.of (Sum.inr (x + y))) =
    AddMonoid.Coprod.mk (FreeAddMonoid.of (Sum.inr x) + FreeAddMonoid.of (Sum.inr y))