Theorems · Theorem · functional analysis
TestFunction.fderivCLM_apply
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace ℝ E] {Ω : TopologicalSpace.Opens E} {F : Type u_4} [inst_3 : NormedAddCommGroup F]
[inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace 𝕜 F] {n k : ℕ∞} [inst_6 : Algebra ℝ 𝕜] [inst_7 : IsScalarTower ℝ 𝕜 F]
(f : TestFunction Ω F n), ⇑((TestFunction.fderivCLM 𝕜 n k) f) = if k + 1 ≤ n then fderiv ℝ ⇑f else 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Algebrastatement and proof · cited by 11,388
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SetLike.coeproof · cited by 8,199
- ContinuousLinearMapstatement and proof · cited by 5,352
- ENatstatement and proof · cited by 4,985
- IsScalarTowerstatement and proof · cited by 3,896
- TopologicalSpace.Opensstatement and proof · cited by 2,040
Cited by6
Results whose statement or proof uses this declaration.
- TestFunction.lineDerivCLM_applyproof · cited by 2
- TestFunction.lineDerivCLM_addproof · cited by 1
- TestFunction.lineDerivCLM_smulproof · cited by 1
- TestFunction.fderivCLM_ofSupportedInproof · cited by 0
- TestFunction.fderivCLM_apply_of_gtproof · cited by 0
- TestFunction.fderivCLM_apply_of_leproof · cited by 0