Theorems · Theorem · global analysis

VectorField.DifferentiableWithinAt.pullbackWithin

∀ {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] [CompleteSpace E]
  {f : E → F} {V : F → F} {s : Set E} {t : Set F} {x : E},
  DifferentiableWithinAt 𝕜 V t (f x) →
    ContDiffWithinAt 𝕜 2 f s x →
      (fderivWithin 𝕜 f s x).IsInvertible →
        UniqueDiffOn 𝕜 s → x ∈ s → Set.MapsTo f s t → DifferentiableWithinAt 𝕜 (VectorField.pullbackWithin 𝕜 f V s) s x

Defined in

Mathlib.Analysis.Calculus.VectorField

Cited by

0 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace