Theorems · Theorem · global analysis

HasFDerivAt.continuousAlternatingMap_apply_const

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {G : Type u_4}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {x : E} {ι : Type u_5} {c : E → F [⋀^ι]→L[𝕜] G}
  {c' : E →L[𝕜] F [⋀^ι]→L[𝕜] G} [inst_7 : Fintype ι],
  HasFDerivAt c c' x → ∀ (u : ι → F), HasFDerivAt (fun y => (c y) u) (c'.flipAlternating u) x

Defined in

Mathlib.Analysis.Calculus.FDeriv.CompCLM

Cited by

2 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype