Theorems · Theorem · global analysis
ContinuousAffineMap.fderivWithin
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E →ᴬ[𝕜] F)
{x : E} {s : Set E}, UniqueDiffWithinAt 𝕜 s x → fderivWithin 𝕜 (⇑f) s x = f.contLinear- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Affine
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- fderivWithinstatement · cited by 357
- ContinuousAffineMapstatement and proof · cited by 263
- UniqueDiffWithinAtstatement and proof · cited by 252
- ContinuousAffineMap.contLinearstatement and proof · cited by 45
- DifferentiableAt.fderivWithinproof · cited by 9
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