∀ {𝕜 : Type u_1} {E : Type u_2} {inst : SeminormedRing 𝕜} {inst_1 : AddGroup E} {inst_2 : SMul 𝕜 E}
  {inst_3 : TopologicalSpace E} [self : BarrelledSpace 𝕜 E] (p : Seminorm 𝕜 E), LowerSemicontinuous ⇑p → Continuous ⇑p