Theorems · Theorem · real analysis
HasDerivWithinAt.differentiableWithinAt
∀ {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 → DifferentiableWithinAt 𝕜 f s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 19 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.
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
- DifferentiableWithinAtstatement · cited by 453
- HasDerivWithinAtstatement and proof · cited by 333
- HasFDerivWithinAt.differentiableWithinAtproof · cited by 65
Cited by19
Results whose statement or proof uses this declaration.
- HasDerivWithinAt.derivWithinproof · cited by 62
- HasLineDerivWithinAt.lineDifferentiableWithinAtproof · cited by 7
- DifferentiableWithinAt.fun_finsetProdproof · cited by 3
- Real.differentiableWithinAt_arcsin_Iciproof · cited by 2
- Real.differentiableWithinAt_arcsin_Iicproof · cited by 2
- ConvexOn.differentiableWithinAt_Iio_of_mem_interiorproof · cited by 2
- ConvexOn.differentiableWithinAt_Ioi_of_mem_interiorproof · cited by 2
- LineDifferentiableWithinAt.congr_monoproof · cited by 1
- RightDerivMeasurableAux.D_subset_differentiable_setproof · cited by 1
- DifferentiableWithinAt.div_constproof · cited by 1
- ODE.contDiffOn_nat_picard_Iccproof · cited by 1
- DifferentiableWithinAt.fun_divproof · cited by 1