∀ {α : Type u_1} {β : Type u_2} [inst : NormedCommGroup β] (e : α ≃ β),
  e.normedCommGroup =
    { toNorm := (NormedCommGroup.induced α β e.mulEquiv ⋯).toNorm,
      toCommGroup := (NormedCommGroup.induced α β e.mulEquiv ⋯).toCommGroup, toPseudoMetricSpace := e.pseudometricSpace,
      eq_of_dist_eq_zero := ⋯, dist_eq := ⋯ }