Theorems · Theorem · functional analysis

ContinuousLinearEquiv.comp_right_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 : F → G} {s : Set F} {x : E}
  {f' : F →L[𝕜] G}, HasFDerivWithinAt (f ∘ ⇑iso) (f' ∘SL ↑iso) (⇑iso ⁻¹' s) x ↔ HasFDerivWithinAt f f' s (iso x)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

3 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace