Theorems · Theorem · algebraic topology

Bundle.Trivialization.prod_symm_apply_snd

∀ {B : Type u_1} [inst : TopologicalSpace B] {F₁ : Type u_2} [inst_1 : TopologicalSpace F₁] {E₁ : B → Type u_3}
  [inst_2 : TopologicalSpace (Bundle.TotalSpace F₁ E₁)] {F₂ : Type u_4} [inst_3 : TopologicalSpace F₂]
  {E₂ : B → Type u_5} [inst_4 : TopologicalSpace (Bundle.TotalSpace F₂ E₂)]
  (e₁ : Bundle.Trivialization F₁ Bundle.TotalSpace.proj) (e₂ : Bundle.Trivialization F₂ Bundle.TotalSpace.proj)
  [inst_5 : (x : B) → Zero (E₁ x)] [inst_6 : (x : B) → Zero (E₂ x)] (p : B × F₁ × F₂),
  (↑(e₁.prod e₂).symm p).snd = (e₁.symm p.1 p.2.1, e₂.symm p.1 p.2.2)

Defined in

Mathlib.Topology.FiberBundle.Constructions

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceZeroZero