English
Similarly, chartAt(H)(Sum.inr x') is the lift to the right component of chartAt(H x'): chartAt(H)(Sum.inr x') = (chartAt(H x')).lift_openEmbedding (X' := M ⊕ M') IsOpenEmbedding.inr.
Русский
Аналогично, chartAt(H)(Sum.inr x') — ливинг справа от chartAt(H x'): chartAt(H)(Sum.inr x') = (chartAt(H x')).lift_openEmbedding (X' := M ⊕ M') IsOpenEmbedding.inr.
LaTeX
$$$chartAt\,H\,(\mathrm{Sum}.\mathrm{inr}\ x') = (chartAt\,H\ x').\mathrm{lift\_openEmbedding}\ (X' := M \oplus M')\ \mathrm{IsOpenEmbedding.inr}.$$
Lean4
theorem sum_chartAt_inr (x' : M') :
haveI : Nonempty H := nonempty_of_chartedSpace x'
chartAt H (Sum.inr x') = (chartAt H x').lift_openEmbedding (X' := M ⊕ M') IsOpenEmbedding.inr :=
by
simp only [chartAt, sum, nonempty_of_chartedSpace x', ↓reduceDIte]
rfl
