∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : AddCommGroup F] [inst_4 : Module 𝕜 F] [inst_5 : Module ℝ E] [IsScalarTower ℝ 𝕜 E] [inst_7 : Module ℝ F]
  [IsScalarTower ℝ 𝕜 F] [inst_9 : TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousSMul 𝕜 E]
  [LocallyConvexSpace ℝ E] [inst_13 : TopologicalSpace F] [IsTopologicalAddGroup F] [ContinuousSMul 𝕜 F]
  [LocallyConvexSpace ℝ F] {s : Set E},
  Convex ℝ s →
    ∀ (e : E →ₗ[𝕜] F), (∀ (f : StrongDual 𝕜 F), Continuous ⇑(e.dualMap ↑f)) → ⇑e '' closure s ⊆ closure (⇑e '' s)