Theorems · Theorem · global analysis
ContinuousAffineMap.fderiv
∀ {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}, fderiv 𝕜 (⇑f) x = f.contLinear- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Affine
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · 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 · cited by 5,352
- fderivstatement · cited by 398
- ContinuousAffineMapstatement and proof · cited by 263
- HasFDerivAt.fderivproof · cited by 93
- ContinuousAffineMap.contLinearstatement · cited by 45
- ContinuousAffineMap.hasFDerivAtproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- lintegral_fderiv_lineMap_eq_edistproof · cited by 1
- ContinuousAffineMap.fderivWithinproof · cited by 0