Theorems · Theorem · global analysis

VectorField.mlieBracket_add_right

∀ {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] {x : M} {V W W₁ : (x : M) → TangentSpace I x}
  [inst_6 : IsManifold I 2 M] [CompleteSpace E],
  MDiffAt (T% W) x →
    MDiffAt (T% W₁) x →
      VectorField.mlieBracket I V (W + W₁) x = VectorField.mlieBracket I V W x + VectorField.mlieBracket I V W₁ x

Defined in

Mathlib.Geometry.Manifold.VectorField.LieBracket

Cited by

0 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceIsManifoldCompleteSpace