Theorems · Theorem · real analysis

hasFDerivWithinAt_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 : (i : ι) → E → F' i}
  {φ' : (i : ι) → E →L[𝕜] F' i},
  HasFDerivWithinAt (fun x i => φ i x) (ContinuousLinearMap.pi φ') s x ↔ ∀ (i : ι), HasFDerivWithinAt (φ i) (φ' i) s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Prod

Cited by

8 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace