Theorems · Theorem · real analysis

not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {f g : 𝕜 → 𝕜} {a : 𝕜} {s t : Set 𝕜},
  a ∈ s →
    UniqueDiffWithinAt 𝕜 s a →
      HasDerivWithinAt f 0 t (g a) → Set.MapsTo g s t → f ∘ g =ᶠ[nhdsWithin a s] id → ¬DifferentiableWithinAt 𝕜 g s a

Defined in

Mathlib.Analysis.Calculus.Deriv.Inverse

Cited by

0 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedField