Theorems · Theorem · real analysis
HasDerivAt.hasDerivWithinAt
∀ {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}, HasDerivAt f f' x → HasDerivWithinAt f f' s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HasDerivAtstatement and proof · cited by 493
- HasDerivWithinAtstatement · cited by 333
- HasFDerivAt.hasFDerivWithinAtproof · cited by 34
Cited by86
Results whose statement or proof uses this declaration.
- HasDerivAt.comp_hasDerivWithinAtproof · cited by 21
- intervalIntegral.integral_eq_sub_of_hasDerivAtproof · cited by 11
- HasFDerivAt.comp_hasDerivAtproof · cited by 10
- intervalIntegral.integral_eq_sub_of_hasDerivAt_of_leproof · cited by 8
- isIntegralCurveAt_iff_exists_mem_nhdsproof · cited by 5
- integral_cpowproof · cited by 5
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- intervalIntegral.integral_mul_deriv_eq_deriv_mulproof · cited by 4
- hasDerivAt_integral_of_dominated_loc_of_deriv_leproof · cited by 4
- intervalIntegral.integrableOn_deriv_of_nonnegproof · cited by 4
- AffineMap.hasDerivWithinAt_lineMapproof · cited by 3
- intervalIntegral.integral_deriv_smul_comp'proof · cited by 3