∀ {M : Type u_3} {N : Type u_4} {M' : Type u_1} {N' : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N]
  [inst_2 : AddZeroClass M'] [inst_3 : AddZeroClass N'] (f : M →+ M') (g : N →+ N') (x y : M),
  (AddMonoid.Coprod.mk.comp (FreeAddMonoid.map (Sum.map ⇑f ⇑g))) (FreeAddMonoid.of (Sum.inl (x + y))) =
    (AddMonoid.Coprod.mk.comp (FreeAddMonoid.map (Sum.map ⇑f ⇑g)))
      (FreeAddMonoid.of (Sum.inl x) + FreeAddMonoid.of (Sum.inl y))