Theorems · Theorem · real analysis
DifferentiableWithinAt.star
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : StarRing 𝕜] {E : Type u_2} [inst_2 : NormedAddCommGroup E]
[inst_3 : NormedSpace 𝕜 E] {F : Type u_3} [inst_4 : NormedAddCommGroup F] [inst_5 : StarAddMonoid F]
[inst_6 : NormedSpace 𝕜 F] [StarModule 𝕜 F] [ContinuousStar F] {f : E → F} {x : E} {s : Set E} [TrivialStar 𝕜],
DifferentiableWithinAt 𝕜 f s x → DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Star
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- StarRingstatement and proof · cited by 1,686
- Star.starstatement · cited by 1,082
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- DifferentiableWithinAtstatement and proof · cited by 453
- StarAddMonoidstatement and proof · cited by 296
- DifferentiableWithinAt.hasFDerivWithinAtproof · cited by 132
- TrivialStarstatement and proof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- DifferentiableOn.starproof · cited by 0