Theorems · Theorem · real analysis

fderivWithin_fderivWithin_eq_of_mem_nhdsWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s t : Set E} {f : E → F}
  {x : E},
  t ∈ nhdsWithin x s →
    ContDiffWithinAt 𝕜 2 f t x →
      UniqueDiffOn 𝕜 s →
        UniqueDiffOn 𝕜 t → x ∈ s → fderivWithin 𝕜 (fderivWithin 𝕜 f s) s x = fderivWithin 𝕜 (fderivWithin 𝕜 f t) t x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Symmetric

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace