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nomeata committed Apr 26, 2024
1 parent a0e61da commit f41ecae
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Showing 2 changed files with 3 additions and 3 deletions.
4 changes: 2 additions & 2 deletions Mathlib/Geometry/Manifold/ChartedSpace.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1189,15 +1189,15 @@ protected instance instChartedSpace : ChartedSpace H s where
lemma chart_eq {s : Opens M} (hs : Nonempty s) {e : PartialHomeomorph s H} (he : e ∈ atlas H s) :
∃ x : s, e = (chartAt H (x : M)).subtypeRestr hs := by
rcases he with ⟨xset, ⟨x, hx⟩, he⟩
exact ⟨x, mem_singleton_iff.mp (by convert hx ▸ he)⟩
exact ⟨x, mem_singleton_iff.mp (by convert he)⟩

/-- If `t` is a non-empty open subset of `H`,
every chart of `t` is the restriction of some chart on `H`. -/
-- XXX: can I unify this with `chart_eq`?
lemma chart_eq' {t : Opens H} (ht : Nonempty t) {e' : PartialHomeomorph t H}
(he' : e' ∈ atlas H t) : ∃ x : t, e' = (chartAt H ↑x).subtypeRestr ht := by
rcases he' with ⟨xset, ⟨x, hx⟩, he'⟩
exact ⟨x, mem_singleton_iff.mp (by convert hx ▸ he')⟩
exact ⟨x, mem_singleton_iff.mp (by convert he')⟩

/-- If a groupoid `G` is `ClosedUnderRestriction`, then an open subset of a space which is
`HasGroupoid G` is naturally `HasGroupoid G`. -/
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2 changes: 1 addition & 1 deletion Mathlib/RingTheory/Ideal/Colon.lean
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Expand Up @@ -29,7 +29,7 @@ def colon (N P : Submodule R M) : Ideal R :=
theorem mem_colon {r} : r ∈ N.colon P ↔ ∀ p ∈ P, r • p ∈ N :=
mem_annihilator.trans
fun H p hp => (Quotient.mk_eq_zero N).1 (H (Quotient.mk p) (mem_map_of_mem hp)),
fun H _ ⟨p, hp, hpm⟩ => hpm ▸ (N.mkQ.map_smul r p ▸ (Quotient.mk_eq_zero N).2 <| H p hp)⟩
fun H _ ⟨p, hp, hpm⟩ => hpm ▸ ((Quotient.mk_eq_zero N).2 <| H p hp)⟩
#align submodule.mem_colon Submodule.mem_colon

theorem mem_colon' {r} : r ∈ N.colon P ↔ P ≤ comap (r • (LinearMap.id : M →ₗ[R] M)) N :=
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