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Merged
pepamontero merged 2 commits into from
Jul 10, 2026
Merged

Change IsManifold from instance to theorem and put the instance after… #2

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4932af4
Change IsManifold from instance to theorem and put the instance after…
qdiazblanco Jul 10, 2026
5ca5d7c
Merge branch 'OrbitSpace-IsManifold' into OrbitSpace-IsManifold-theorem
pepamontero Jul 10, 2026
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16 changes: 12 additions & 4 deletions Mathlib/Geometry/Manifold/Instances/Quotient.lean
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Expand Up @@ -203,9 +203,11 @@ lemma StructureGroupoid.restr_mem_of_eqOn {G : StructureGroupoid X}
end

-- the action is smooth
variable [TopologicalSpace G] [ChartedSpace H G] [ContMDiffSMul I I n G M]
variable {E' : Type*} [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*}
[TopologicalSpace H'] (J : ModelWithCorners 𝕜 E' H') [TopologicalSpace G] [ChartedSpace H' G]

instance : IsManifold I n (orbitRel.Quotient G M) where
theorem isManifold_quotient_of_contMDiffSMul [ContMDiffSMul J I n G M] :
IsManifold I n (orbitRel.Quotient G M) where
compatible := by
rintro _ _ ⟨x, rfl⟩ ⟨y, rfl⟩
rw [(πinv x).trans_symm_eq_symm_trans_symm, (chartAt H x.out).symm.trans_assoc,
Expand All @@ -222,12 +224,18 @@ instance : IsManifold I n (orbitRel.Quotient G M) where
(IsManifold.chart_mem_maximalAtlas x.out) (IsManifold.chart_mem_maximalAtlas y.out) ?_ ?_)
hto (hg0'.mono inter_subset_right) ?_
· rw [Homeomorph.toOpenPartialHomeomorph_apply]
exact (ContMDiffSMul.contMDiff_const_smul (I := I) g0).contMDiffOn
exact (ContMDiffSMul.contMDiff_const_smul (I := J) g0).contMDiffOn
· rw [Homeomorph.toOpenPartialHomeomorph_symm_apply]
exact (ContMDiffSMul.contMDiff_const_smul (I := I) g0⁻¹).contMDiffOn
exact (ContMDiffSMul.contMDiff_const_smul (I := J) g0⁻¹).contMDiffOn
· rintro h' ⟨⟨hQ1, _, hQ4⟩, _, hcert⟩
exact ⟨hQ1, mem_univ _, by simpa [← smul_eqOn x y g0 hcert] using hQ4⟩

open scoped Manifold

attribute [local instance] ChartedSpace.of_discreteTopology
instance [DiscreteTopology G] [ContMDiffSMul 𝓘(𝕜, PUnit) I n G M] :
IsManifold I n (orbitRel.Quotient G M) := isManifold_quotient_of_contMDiffSMul I 𝓘(𝕜, PUnit)

end MulAction

end
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