Theorems · Theorem · functional analysis

ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff

∀ {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] (iso : E ≃L[𝕜] F) {f : G → E} {s : Set G} {x : G}
  {f' : G →L[𝕜] E}, HasFDerivWithinAt (⇑iso ∘ f) (↑iso ∘SL f') s x ↔ HasFDerivWithinAt f f' s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

5 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace