Theorems · Theorem · global analysis

VectorField.pullbackWithin_eq_of_fderivWithin_eq

∀ {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] {s : Set E}
  {f : E → F} {M : E ≃L[𝕜] F} {x : E},
  ↑M = fderivWithin 𝕜 f s x → ∀ (V : F → F), VectorField.pullbackWithin 𝕜 f V s x = M.symm (V (f x))

Defined in

Mathlib.Analysis.Calculus.VectorField

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace