∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {C : AddMonoid.Coprod M N → Prop}
  (m : AddMonoid.Coprod M N),
  (∀ (m : M), C (AddMonoid.Coprod.inl m)) →
    (∀ (n : N), C (AddMonoid.Coprod.inr n)) → (∀ (x y : AddMonoid.Coprod M N), C x → C y → C (x + y)) → C m