∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f f' : ℝ → E} {C : ℝ},
  (∀ x ∈ Set.Icc 0 1, HasDerivWithinAt f (f' x) (Set.Icc 0 1) x) → (∀ x ∈ Set.Ico 0 1, ‖f' x‖ ≤ C) → ‖f 1 - f 0‖ ≤ C