∀ (𝕜 : Type u_1) (E : Type u_2) (F : Type u_3) {ι : Type u_4} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] [inst_7 : IsTopologicalAddGroup F] [inst_8 : ContinuousConstSMul 𝕜 F]
  [inst_9 : ContinuousSMul 𝕜 E] (m m_1 : ι → E),
  m = m_1 → ContinuousAlternatingMap.apply 𝕜 E F m = ContinuousAlternatingMap.apply 𝕜 E F m_1