Theorems · Theorem · real analysis
HasCompactSupport.fderiv_apply
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F},
HasCompactSupport f → ∀ (v : E), HasCompactSupport fun x => (fderiv 𝕜 f x) v- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Const
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 176 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.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- fderivstatement and proof · cited by 398
- HasCompactSupportstatement and proof · cited by 196
- IsCompact.of_isClosed_subsetproof · cited by 67
- isClosed_tsupportproof · cited by 17
- tsupport_fderiv_apply_subsetproof · cited by 5
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