Theorems · Theorem · real analysis

IsOpen.exists_eq_add_of_deriv_eq

∀ {𝕜 : Type u_3} {G : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup G] [inst_2 : NormedSpace 𝕜 G] {s : Set 𝕜}
  {f g : 𝕜 → G},
  IsOpen s →
    IsPreconnected s →
      DifferentiableOn 𝕜 f s →
        DifferentiableOn 𝕜 g s → Set.EqOn (deriv f) (deriv g) s → ∃ a, Set.EqOn f (fun x => g x + a) s

Defined in

Mathlib.Analysis.Calculus.MeanValue

Cited by

0 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpace