Theorems · Theorem · global analysis
toDual_comp_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} {s : Set F},
⇑(InnerProductSpace.toDual 𝕜 F) ∘ gradientWithin f s = fderivWithin 𝕜 f s- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 459
- fderivWithinstatement · cited by 357
- InnerProductSpace.toDualstatement · cited by 45
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