∀ {X : Type u_1} {R : Type u_2} [inst : Zero X] [inst_1 : Zero R] [inst_2 : TopologicalSpace X]
  [inst_3 : TopologicalSpace R] (toContinuousMap toContinuousMap_1 : C(X, R))
  (e_toContinuousMap : toContinuousMap = toContinuousMap_1) (map_zero' : toContinuousMap 0 = 0),
  { toContinuousMap := toContinuousMap, map_zero' := map_zero' } =
    { toContinuousMap := toContinuousMap_1, map_zero' := ⋯ }