∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_2} [inst_1 : AddGroup N] (f : G →+ N) (H : AddSubgroup N) {a b : G},
  a ∈ (AddSubmonoid.comap f H.toAddSubmonoid).carrier →
    b ∈ (AddSubmonoid.comap f H.toAddSubmonoid).carrier → a + b ∈ (AddSubmonoid.comap f H.toAddSubmonoid).carrier