Theorems · Theorem · real analysis
hasDerivWithinAt_univ
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜}, HasDerivWithinAt f f' Set.univ x ↔ HasDerivAt f f' x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 155 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univstatement · cited by 3,945
- HasDerivAtstatement · cited by 493
- HasDerivWithinAtstatement · cited by 333
- hasFDerivWithinAt_univproof · cited by 14
Cited by18
Results whose statement or proof uses this declaration.
- HasDerivAt.const_mulproof · cited by 25
- HasDerivAt.mulproof · cited by 20
- HasFDerivAt.comp_hasDerivAtproof · cited by 10
- HasDerivAt.mul_constproof · cited by 8
- HasDerivAt.smul_constproof · cited by 7
- HasDerivAt.tendsto_nhdsNEproof · cited by 5
- HasDerivAt.invproof · cited by 5
- HasDerivAt.logproof · cited by 4
- HasDerivAt.smulproof · cited by 4
- HasDerivAt.rpow_constproof · cited by 2
- HasDerivAt.const_rpowproof · cited by 1
- HasDerivAt.rpowproof · cited by 1