English
Given a homeomorphism e: X ≃ₜ Y, there is an equivalence between LocallyConstant X Z and LocallyConstant Y Z, induced by pulling back along e.
Русский
Дано фронтома \(e: X \\simeq_t Y\), существует эквивалентность между LocallyConstant X Z и LocallyConstant Y Z, получаемая вытаскиванием вдоль e.
LaTeX
$$$ \\text{congrLeft } (e) : LocallyConstant X Z \\simeq LocallyConstant Y Z $$$
Lean4
/-- The equivalence between `LocallyConstant X Z` and `LocallyConstant Y Z` given a
homeomorphism `X ≃ₜ Y`
-/
@[simps]
def congrLeft [TopologicalSpace Y] (e : X ≃ₜ Y) : LocallyConstant X Z ≃ LocallyConstant Y Z
where
toFun := comap e.symm
invFun := comap e
left_inv := by
intro
simp [comap_comap]
right_inv := by
intro
simp [comap_comap]
