Theorems · Theorem · real analysis

IsOpen.exists_eq_add_of_fderiv_eq

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [NormedSpace ℝ E] {𝕜 : Type u_3} {G : Type u_4}
  [inst_2 : NontriviallyNormedField 𝕜] [IsRCLikeNormedField 𝕜] [inst_4 : NormedSpace 𝕜 E]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f g : E → G} {s : Set E},
  IsOpen s →
    IsPreconnected s →
      DifferentiableOn 𝕜 f s →
        DifferentiableOn 𝕜 g s → Set.EqOn (fderiv 𝕜 f) (fderiv 𝕜 g) s → ∃ a, Set.EqOn f (fun x => g x + a) s

Defined in

Mathlib.Analysis.Calculus.MeanValue

Cited by

2 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNontriviallyNormedFieldIsRCLikeNormedFieldNormedSpaceNormedAddCommGroupNormedSpace