Theorems · Theorem · real analysis
DifferentiableWithinAt.hasDerivWithinAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜},
DifferentiableWithinAt 𝕜 f s x → HasDerivWithinAt f (derivWithin f s x) s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 85 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
- DifferentiableWithinAtstatement and proof · cited by 453
- HasDerivWithinAtstatement · cited by 333
- derivWithinstatement · cited by 258
- DifferentiableWithinAt.hasFDerivWithinAtproof · cited by 132
- HasFDerivWithinAt.hasDerivWithinAtproof · cited by 14
Cited by85
Results whose statement or proof uses this declaration.
- HasDerivWithinAt.derivWithinproof · cited by 62
- LineDifferentiableWithinAt.hasLineDerivWithinAtproof · cited by 9
- MonotoneOn.derivWithin_nonnegproof · cited by 4
- DifferentiableWithinAt.fun_finsetProdproof · cited by 3
- range_derivWithin_subset_closure_span_imageproof · cited by 3
- taylor_isLittleOproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2
- Manifold.pathELength_comp_of_monotoneOnproof · cited by 2
- Real.differentiableWithinAt_arcsin_Iciproof · cited by 2
- derivWithin_Ioi_eq_Iciproof · cited by 2
- derivWithin.scompproof · cited by 2
- derivWithin_fun_addproof · cited by 2