Theorems · Theorem · global analysis
DifferentiableWithinAt.hasGradientWithinAt
∀ {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} {x : F} {s : Set F},
DifferentiableWithinAt 𝕜 f s x → HasGradientWithinAt f (gradientWithin f s x) s x- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- DifferentiableWithinAtstatement and proof · cited by 453
- HasFDerivWithinAtproof · cited by 356
- DifferentiableWithinAt.hasFDerivWithinAtproof · cited by 132
- HasGradientWithinAtstatement · cited by 20
- gradientWithinstatement · cited by 7
- toDual_gradientWithinproof · cited by 2
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