Theorems · Theorem · global analysis
HasGradientWithinAt.fderivWithin_apply
∀ {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 y : F} {s : Set F},
HasGradientWithinAt f f' s x → UniqueDiffWithinAt 𝕜 s x → (fderivWithin 𝕜 f s x) y = inner 𝕜 f' y- 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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Cites15
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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- Inner.innerstatement and proof · cited by 1,089
- fderivWithinstatement · cited by 357
- UniqueDiffWithinAtstatement and proof · cited by 252
- HasFDerivWithinAt.fderivWithinproof · cited by 69
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