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Theorems · Theorem · global analysis

HasGradientWithinAt.differentiableWithinAt

∀ {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} {s : Set F},
  HasGradientWithinAt f f' s x → DifferentiableWithinAt 𝕜 f 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
Assumes
RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace
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Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeCompleteSpace · cited by 2532CompleteSpaceDifferentiableWithinAt · cited by 453DifferentiableWithinAtHasFDerivWithinAt.differentiableWithinAt · cited by 65HasFDerivWithinAt.differe…HasGradientWithinAt · cited by 20HasGradientWithinAtHasGradientWithinAt.hasFDerivWithinAt · cited by 2HasGradientWithinAt.hasFD…HasGradientWithinAt.different…CITED BYCITES

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