Theorems · Theorem · real analysis
hasStrictDerivAt_abs
∀ {x : ℝ}, x ≠ 0 → HasStrictDerivAt (fun x => |x|) (↑(SignType.sign x)) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- absstatement and proof · cited by 1,814
- OrderHomstatement · cited by 934
- SignTypestatement · cited by 318
- HasStrictDerivAtstatement · cited by 163
- SignType.signstatement and proof · cited by 128
- Ne.lt_or_gtproof · cited by 108
- SignType.caststatement and proof · cited by 76
- sign_posproof · cited by 49
- HasStrictDerivAt.congr_simpproof · cited by 41
- sign_negproof · cited by 35
Cited by2
Results whose statement or proof uses this declaration.
- hasDerivAt_absproof · cited by 5
- HasStrictFDerivAt.absproof · cited by 0