Theorems · Theorem · real analysis
derivWithin_zero_of_not_accPt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜}, ¬AccPt x (Filter.principal s) → derivWithin f s x = 0- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapproof · cited by 5,352
- Filter.principalstatement and proof · cited by 740
- derivWithinstatement · cited by 258
- zero_applyproof · cited by 251
- AccPtstatement and proof · cited by 75
- fderivWithin_zero_of_not_accPtproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- derivWithin_zero_of_not_uniqueDiffWithinAtproof · cited by 26
- iteratedDerivWithin_succproof · cited by 11
- iteratedDerivWithin_oneproof · cited by 6
- MonotoneOn.derivWithin_nonnegproof · cited by 4