Theorems · Theorem · real analysis
HasDerivWithinAt.hasDerivAt
∀ {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 → s ∈ nhds x → HasDerivAt f f' x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- HasDerivAtstatement · cited by 493
- HasDerivWithinAtstatement and proof · cited by 333
- HasFDerivWithinAt.hasFDerivAtproof · cited by 6
Cited by18
Results whose statement or proof uses this declaration.
- isIntegralCurveAt_iff_exists_mem_nhdsproof · cited by 5
- HasLineDerivWithinAt.hasLineDerivAt'proof · cited by 2
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- isIntegralCurveOn_univproof · cited by 2
- HasDerivWithinAt.lhopital_zero_nhdsWithin_convexproof · cited by 1
- intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAtproof · cited by 1
- intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAtproof · cited by 1
- derivWithin_tsumproof · cited by 1
- ODE.picard_eq_of_hasDerivAtproof · cited by 1
- isIntegralCurveAt_iff_exists_posproof · cited by 1
- intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAtproof · cited by 1