Theorems · Theorem · algebraic topology

Bundle.Pretrivialization.continuousAlternatingMap.congr_simp

∀ (𝕜 : Type u_1) (ι : Type u_2) [inst : NontriviallyNormedField 𝕜] {B : Type u_3} [inst_1 : TopologicalSpace B]
  {F₁ : Type u_4} [inst_2 : NormedAddCommGroup F₁] [inst_3 : NormedSpace 𝕜 F₁] {E₁ : B → Type u_5}
  [inst_4 : (x : B) → AddCommGroup (E₁ x)] [inst_5 : (x : B) → Module 𝕜 (E₁ x)]
  [inst_6 : TopologicalSpace (Bundle.TotalSpace F₁ E₁)] {F₂ : Type u_6} [inst_7 : NormedAddCommGroup F₂]
  [inst_8 : NormedSpace 𝕜 F₂] {E₂ : B → Type u_7} [inst_9 : (x : B) → AddCommGroup (E₂ x)]
  [inst_10 : (x : B) → Module 𝕜 (E₂ x)] [inst_11 : TopologicalSpace (Bundle.TotalSpace F₂ E₂)]
  [inst_12 : (x : B) → TopologicalSpace (E₁ x)] [inst_13 : FiberBundle F₁ E₁]
  [inst_14 : (x : B) → TopologicalSpace (E₂ x)] [inst_15 : FiberBundle F₂ E₂]
  (e₁ e₁_1 : Bundle.Trivialization F₁ Bundle.TotalSpace.proj) (e_e₁ : e₁ = e₁_1)
  (e₂ e₂_1 : Bundle.Trivialization F₂ Bundle.TotalSpace.proj) (e_e₂ : e₂ = e₂_1)
  [inst_16 : Bundle.Trivialization.IsLinear 𝕜 e₁] [inst_17 : Bundle.Trivialization.IsLinear 𝕜 e₂],
  Bundle.Pretrivialization.continuousAlternatingMap 𝕜 ι e₁ e₂ =
    Bundle.Pretrivialization.continuousAlternatingMap 𝕜 ι e₁_1 e₂_1

Defined in

Mathlib.Topology.VectorBundle.ContinuousAlternatingMap

Cited by

0 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceAddCommGroupModuleTopologicalSpaceNormedAddCommGroupNormedSpaceAddCommGroupModuleTopologicalSpaceTopologicalSpaceFiberBundleTopologicalSpaceFiberBundleBundle.Trivialization.IsLinearBundle.Trivialization.IsLinear