Theorems · Theorem · real analysis

UniqueDiffWithinAt.eq_deriv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' f₁' : F} {x : 𝕜} (s : Set 𝕜),
  UniqueDiffWithinAt 𝕜 s x → HasDerivWithinAt f f' s x → HasDerivWithinAt f f₁' s x → f' = f₁'

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

6 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace