Theorems · Theorem · global analysis

Bundle.Trivialization.localFrame_apply_of_mem_baseSet

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {M : Type u_4} [inst_1 : TopologicalSpace M] {F : Type u_5}
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 F] {V : M → Type u_6}
  [inst_4 : TopologicalSpace (Bundle.TotalSpace F V)] [inst_5 : (x : M) → AddCommGroup (V x)]
  [inst_6 : (x : M) → Module 𝕜 (V x)] [inst_7 : (x : M) → TopologicalSpace (V x)] [inst_8 : FiberBundle F V]
  [inst_9 : VectorBundle 𝕜 F V] {ι : Type u_7} {x : M} (e : Bundle.Trivialization F Bundle.TotalSpace.proj)
  [inst_10 : MemTrivializationAtlas e] (b : Module.Basis ι 𝕜 F) {i : ι} (hx : x ∈ e.baseSet),
  e.localFrame b i x = (e.basisAt b hx) i

Defined in

Mathlib.Geometry.Manifold.VectorBundle.LocalFrame

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceAddCommGroupModuleTopologicalSpaceFiberBundleVectorBundleMemTrivializationAtlas