∀ {M : Type u_1} {N : Type u_2} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] [inst_2 : AddMonoid P]
  (f : M →+ P) (g : N →+ P) (x : FreeAddMonoid (M ⊕ N)),
  (AddMonoid.Coprod.lift f g) (AddMonoid.Coprod.mk x) = (FreeAddMonoid.lift (Sum.elim ⇑f ⇑g)) x