Theorems · Theorem · real analysis
HasDerivWithinAt.neg
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜} {s : Set 𝕜},
HasDerivWithinAt f f' s x → HasDerivWithinAt (-f) (-f') s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- HasDerivWithinAtstatement and proof · cited by 333
- HasDerivAtFilter.negproof · cited by 7
Cited by14
Results whose statement or proof uses this declaration.
- ConcaveOn.le_slope_of_hasDerivWithinAt_Iioproof · cited by 3
- ConcaveOn.slope_le_of_hasDerivWithinAt_Ioiproof · cited by 3
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_antitoneOnproof · cited by 2
- StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iioproof · cited by 2
- intervalIntegral.integral_le_sub_of_hasDeriv_right_of_leproof · cited by 2
- MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOnproof · cited by 2
- intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_leftproof · cited by 2
- StrictConcaveOn.lt_slope_of_hasDerivWithinAtproof · cited by 1
- HasDerivWithinAt.nonpos_of_antitoneOnproof · cited by 1
- exists_hasDerivWithinAt_eq_of_lt_of_gtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivWithinAtproof · cited by 1