Theorems · Theorem · real analysis

IsOpen.is_const_of_deriv_eq_zero

∀ {𝕜 : Type u_3} {G : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup G] [inst_2 : NormedSpace 𝕜 G] {f : 𝕜 → G}
  {s : Set 𝕜},
  IsOpen s → IsPreconnected s → DifferentiableOn 𝕜 f s → Set.EqOn (deriv f) 0 s → ∀ {x y : 𝕜}, x ∈ s → y ∈ s → f x = f y

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