Theorems · Theorem · real analysis

IsOpen.exists_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 → ∃ a, ∀ x ∈ s, f x = a

Defined in

Mathlib.Analysis.Calculus.MeanValue

Cited by

1 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupNormedSpace