∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_3}
  [inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] {f : F},
  Function.Injective ⇑f → ∀ (S : AddSubmonoid M), ∀ x ∈ AddSubmonoid.comap f (AddSubmonoid.map f S), x ∈ S