∀ {M : Type u_1} {N : Type u_2} {F : Type u_5} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N]
  [inst_2 : FunLike F M N] [AddMonoidHomClass F M N] {s : Set M}, IsLinearSet s → ∀ (f : F), IsLinearSet (⇑f '' s)