Theorems · Theorem · real analysis
HasFDerivAt.abs_of_neg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E},
HasFDerivAt f f' x → f x < 0 → HasFDerivAt (fun x => |f x|) (-f') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Abs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldproof · cited by 8,742
- ContinuousLinearMapproof · cited by 5,352
- mul_oneproof · cited by 3,885
- absstatement and proof · cited by 1,814
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.