Theorems · Theorem · global analysis
HasGradientAt.differentiableAt
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup F] [inst_2 : InnerProductSpace 𝕜 F]
[inst_3 : CompleteSpace F] {f : F → 𝕜} {f' x : F}, HasGradientAt f f' x → DifferentiableAt 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- DifferentiableAtstatement · cited by 617
- HasFDerivAt.differentiableAtproof · cited by 83
- HasGradientAtstatement and proof · cited by 24
- HasGradientAt.hasFDerivAtproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- HasGradientAt.gradientproof · cited by 1