instClosedUnderRestrictionContDiffGroupoid

English

Building a C^n manifold from a HasGroupoid hypothesis yields IsManifold.

Русский

Построение C^n-ман sovrem из предположения HasGroupoid дает IsManifold.

LaTeX

$$$\text{IsManifold I n M}$ from $gr : HasGroupoid M (contDiffGroupoid n I)$$$

Lean4

/-- The `C^n` groupoid is closed under restriction. -/
instance : ClosedUnderRestriction (contDiffGroupoid n I) :=
  (closedUnderRestriction_iff_id_le _).mpr
    (by
      rw [StructureGroupoid.le_iff]
      rintro e ⟨s, hs, hes⟩
      apply (contDiffGroupoid n I).mem_of_eqOnSource' _ _ _ hes
      exact ofSet_mem_contDiffGroupoid hs)

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