Theorems · Theorem · functional analysis
TestFunction.lineDerivCLM_apply_of_le
∀ {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} {v x : E}, k + 1 ≤ n → ((TestFunction.lineDerivCLM 𝕜 v) f) x = lineDeriv ℝ (⇑f) x v- Cited by
- 0 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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 · 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
- ContinuousLinearMapstatement · 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
- TestFunctionstatement and proof · cited by 76
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