Theorems · Theorem · real analysis
DifferentiableWithinAt.abs_of_neg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {x : E},
DifferentiableWithinAt ℝ f s x → f x < 0 → DifferentiableWithinAt ℝ (fun x => |f x|) s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Abs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- absstatement · cited by 1,814
- DifferentiableWithinAtstatement and proof · cited by 453
- DifferentiableAt.comp_differentiableWithinAtproof · cited by 14
- differentiableAt_abs_negproof · cited by 3
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