Theorems · Theorem · real analysis
differentiableWithinAt_inv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedDivisionRing R]
[inst_2 : NormedAlgebra 𝕜 R] {x : R}, x ≠ 0 → ∀ (s : Set R), DifferentiableWithinAt 𝕜 (fun x => x⁻¹) s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableWithinAtstatement · cited by 453
- NormedDivisionRingstatement and proof · cited by 360
- DifferentiableAt.differentiableWithinAtproof · cited by 96
- differentiableAt_invproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- differentiableOn_invproof · cited by 1