Theorems · Theorem · global analysis
VectorField.lieBracketWithin_inter
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {V W : E → E} {s t : Set E} {x : E},
t ∈ nhds x → VectorField.lieBracketWithin 𝕜 V W (s ∩ t) x = VectorField.lieBracketWithin 𝕜 V W s x- Defined in
- Mathlib.Analysis.Calculus.VectorField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · 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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- fderivWithinproof · cited by 357
- VectorField.lieBracketWithinstatement · cited by 57
- fderivWithin_interproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- VectorField.lieBracketWithin_of_mem_nhdsproof · cited by 1