Theorems · Theorem · real analysis

ContDiffAt.fderiv_right

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x₀ : E}
  {m n : WithTop ℕ∞}, ContDiffAt 𝕜 n f x₀ → m + 1 ≤ n → ContDiffAt 𝕜 m (fderiv 𝕜 f) x₀

fderiv 𝕜 f is smooth at x₀.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

5 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace