Theorems · Theorem · real analysis
deriv_of_notMem_tsupport
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜}, x ∉ tsupport f → deriv f x = 0- Defined in
- Mathlib.Analysis.Calculus.Deriv.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- derivstatement · cited by 676
- tsupportstatement and proof · cited by 178
- Filter.EventuallyEq.deriv_eqproof · cited by 14
- notMem_tsupport_iff_eventuallyEqproof · cited by 7
- deriv_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- support_deriv_subsetproof · cited by 2