∀ {F : Type u_1} {G : Type u_2} {M : Type u_3} {N : Type u_4} [inst : FunLike F M N] [inst_1 : FunLike G N M]
  [inst_2 : AddMonoid M] [inst_3 : AddMonoid N] [AddMonoidHomClass F M N] [AddMonoidHomClass G N M] {f : F} {x : M}
  (g : G), Function.LeftInverse ⇑g ⇑f → (IsAddUnit (f x) ↔ IsAddUnit x)