English
On the domain of the product trivialization, applying invFun' after toFun' recovers the original element.
Русский
На области определения произведения тривиализации применение invFun' после toFun' восстанавливает исходный элемент.
LaTeX
$$$\forall x \in \pi^{-1}'(e_1.baseSet \cap e_2.baseSet),\ Prod.invFun'(e_1,e_2)(Prod.toFun'(e_1,e_2)(x)) = x$$$
Lean4
/-- Given trivializations `e₁`, `e₂` for fiber bundles `E₁`, `E₂` over a base `B`, the inverse
function for the construction `Trivialization.prod`, the induced
trivialization for the fiberwise product of `E₁` and `E₂`. -/
noncomputable def invFun' (p : B × F₁ × F₂) : TotalSpace (F₁ × F₂) (E₁ ×ᵇ E₂) :=
⟨p.1, e₁.symm p.1 p.2.1, e₂.symm p.1 p.2.2⟩