∀ (𝕜 : Type u_1) (E : Type u_2) [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [IsTopologicalAddGroup E] {ι : Type u_3} (b : ι → Set E)
  (p : ι → Prop), (nhds 0).HasBasis p b → (∀ (i : ι), p i → Convex 𝕜 (b i)) → LocallyConvexSpace 𝕜 E