Theorems · Theorem · global analysis

VectorField.mlieBracketWithin_zero_left

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {W : (x : M) → TangentSpace I x},
  VectorField.mlieBracketWithin I 0 W s = 0

We have [0, W] = 0 for all vector fields W: this depends on the junk value 0 if W is not differentiable. Version within a set.

Defined in

Mathlib.Geometry.Manifold.VectorField.LieBracket

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpace