Theorems · Theorem · real analysis
HasDerivAt.sub
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜},
HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (f - g) (f' - g') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 15 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- HasDerivAtstatement and proof · cited by 493
- HasDerivAtFilter.subproof · cited by 4
Cited by15
Results whose statement or proof uses this declaration.
- deriv_fun_subproof · cited by 12
- InformationTheory.hasDerivAt_klFunproof · cited by 3
- exists_ratio_hasDerivAt_eq_ratio_slopeproof · cited by 3
- intervalIntegral.intervalIntegrable_log'proof · cited by 2
- Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_rangeproof · cited by 2
- exists_ratio_hasDerivAt_eq_ratio_slope'proof · cited by 2
- norm_image_sub_le_of_norm_deriv_right_le_segmentproof · cited by 2
- deriv_subproof · cited by 1
- AbsolutelyContinuousOnInterval.integral_deriv_eq_subproof · cited by 1
- Complex.hasDerivAt_log_sub_logTaylorproof · cited by 1
- integral_log_from_zero_of_posproof · cited by 1
- BoundedVariationOn.intervalIntegrable_derivproof · cited by 1