Theorems · Theorem · real analysis
derivWithin_inter
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s t : Set 𝕜}, t ∈ nhds x → derivWithin f (s ∩ t) x = derivWithin f s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHom.idproof · 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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- ContinuousLinearMapproof · cited by 5,352
- fderivWithinproof · cited by 357
- derivWithinstatement · cited by 258
- fderivWithin_interproof · cited by 6
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