Theorems · Theorem · functional analysis
HasFDerivAt.hasFDerivAt_norm_smul_neg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : StrongDual ℝ E} {x : E} {t : ℝ},
t < 0 → HasFDerivAt (fun x => ‖x‖) f x → HasFDerivAt (fun x => ‖x‖) (-f) (t • x)- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Norm
- Cited by
- 0 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- one_smulproof · cited by 1,374
- LT.lt.neproof · cited by 872
- StrongDualstatement and proof · cited by 459
- HasFDerivAtstatement and proof · cited by 350
- neg_smulproof · cited by 306
- SignType.castproof · cited by 76
- sign_negproof · cited by 35
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.