Theorems · Theorem · real analysis

differentiableWithinAt_pi

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {s : Set E} {ι : Type u_6} {F' : ι → Type u_7}
  [inst_3 : (i : ι) → NormedAddCommGroup (F' i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (F' i)] {Φ : E → (i : ι) → F' i},
  DifferentiableWithinAt 𝕜 Φ s x ↔ ∀ (i : ι), DifferentiableWithinAt 𝕜 (fun x => Φ x i) s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Prod

Cited by

6 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace