English
The identity transformation on the model with corners is smooth of order n.
Русский
Идентичность на модели с углами гладна порядка n.
LaTeX
$$$\mathrm{ContMDiff}\, I\, 𝓘(\mathbb{C}, E)\, n\, I$$$
Lean4
theorem contMDiff_model : ContMDiff I 𝓘(𝕜, E) n I := by
intro x
refine contMDiffAt_iff.mpr ⟨I.continuousAt, ?_⟩
simp only [mfld_simps]
refine contDiffWithinAt_id.congr_of_eventuallyEq ?_ ?_
· exact Filter.eventuallyEq_of_mem self_mem_nhdsWithin fun x₂ => I.right_inv
simp_rw [Function.comp_apply, I.left_inv, Function.id_def]