Theorems · Theorem · global analysis
toDual_gradientWithin
∀ {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},
(InnerProductSpace.toDual 𝕜 F) (gradientWithin f s x) = fderivWithin 𝕜 f s x- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHom.idstatement · cited by 18,349
- 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
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- StrongDualstatement and proof · cited by 459
- fderivWithinstatement and proof · cited by 357
- InnerProductSpace.toDualstatement and proof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.hasGradientWithinAtproof · cited by 0
- toDual_comp_gradientWithinproof · cited by 0