∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [t : TopologicalSpace E] [IsTopologicalAddGroup E] (p : SeminormFamily 𝕜 E ι),
  (nhds 0).HasBasis (fun s => s ∈ p.basisSets) id → WithSeminorms p