Theorems · Theorem · global analysis

VectorField.mlieBracketWithin_congr

∀ {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} {x : M}
  {V W V₁ W₁ : (x : M) → TangentSpace I x},
  Set.EqOn V₁ V s →
    V₁ x = V x →
      Set.EqOn W₁ W s → W₁ x = W x → VectorField.mlieBracketWithin I V₁ W₁ s x = VectorField.mlieBracketWithin I V W s x

Defined in

Mathlib.Geometry.Manifold.VectorField.LieBracket

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpace