Theorems · Theorem · functional analysis

ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff

∀ {𝕜 : Type u_1} {ι : Type u_2} {E : Type u_3} {G : Type u_5} {H : Type u_6} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G]
  [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H] {f : E → G [⋀^ι]→L[𝕜] H} {f' : E →L[𝕜] G [⋀^ι]→L[𝕜] H}
  {x : E} [Finite ι],
  HasStrictFDerivAt (ContinuousAlternatingMap.toContinuousMultilinearMap ∘ f)
      (ContinuousAlternatingMap.toContinuousMultilinearMapCLM 𝕜 ∘SL f') x ↔
    HasStrictFDerivAt f f' x

Defined in

Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFinite