Theorems · Theorem · real analysis
IsSymmSndFDerivAt.isSymmSndFDerivWithinAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E} {f : E → F} {x : E},
IsSymmSndFDerivAt 𝕜 f x → ContDiffAt 𝕜 2 f x → UniqueDiffOn 𝕜 s → x ∈ s → IsSymmSndFDerivWithinAt 𝕜 f s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement · cited by 4,985
- WithTopstatement · cited by 3,754
- ContDiffAtstatement and proof · cited by 262
- UniqueDiffOnstatement and proof · cited by 215
- Filter.univ_memproof · cited by 96
- uniqueDiffOn_univproof · cited by 66
- IsSymmSndFDerivWithinAtstatement · cited by 16
- IsSymmSndFDerivAtstatement and proof · cited by 10
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