English
The prod construction on model-with-corners respects the toPartialEquiv map: (I.prod J).toPartialEquiv = I.toPartialEquiv.prod J.toPartialEquiv.
Русский
Произведение моделей с углами сохраняет отображение toPartialEquiv: (I.prod J).toPartialEquiv = I.toPartialEquiv.prod J.toPartialEquiv.
LaTeX
$$$$ (I.prod J).toPartialEquiv = I.toPartialEquiv.prod J.toPartialEquiv. $$$$
Lean4
theorem map_extChartAt_nhdsWithin_eq_image' {x y : M} (hy : y ∈ (extChartAt I x).source) :
map (extChartAt I x) (𝓝[s] y) = 𝓝[extChartAt I x '' ((extChartAt I x).source ∩ s)] extChartAt I x y :=
map_extend_nhdsWithin_eq_image _ <| by rwa [← extChartAt_source I]