Theorems · Theorem · real analysis

ContDiffWithinAt.fun_inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {s : Set E} {x : E} {𝕜' : Type u_4} [inst_3 : NormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
  {f : E → 𝕜'} {n : WithTop ℕ∞}, ContDiffWithinAt 𝕜 n f s x → f x ≠ 0 → ContDiffWithinAt 𝕜 n (fun i => (f i)⁻¹) s x

Eta-expanded form of ContDiffWithinAt.inv

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedFieldNormedAlgebra