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fix
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YaelDillies committed Jan 7, 2025
1 parent 0b689e8 commit c2b4440
Showing 1 changed file with 5 additions and 4 deletions.
9 changes: 5 additions & 4 deletions Mathlib/Topology/Constructible.lean
Original file line number Diff line number Diff line change
Expand Up @@ -344,9 +344,10 @@ lemma IsConstructible.induction_of_isTopologicalBasis {ι : Type*} [Nonempty ι]
basis.isConstructible compact_inter _))
(union : ∀ s hs t ht, P s hs → P t ht → P (s ∪ t) (hs.union ht))
(s : Set X) (hs : IsConstructible s) : P s hs := by
induction hs using BooleanSubalgebra.closure_sdiff_sup_induction with
| sup => exact fun s hs t ht ↦ ⟨hs.1.union ht.1, hs.2.union ht.2
| inf => exact fun s hs t ht ↦ ⟨hs.1.inter ht.1, hs.2.inter_isOpen ht.2 ht.1
induction s, hs using BooleanSubalgebra.closure_sdiff_sup_induction with
| isSublattice =>
exact ⟨fun s hs t ht ↦ ⟨hs.1.union ht.1, hs.2.union ht.2⟩,
fun s hs t ht ↦ ⟨hs.1.inter ht.1, hs.2.inter_isOpen ht.2 ht.1⟩⟩
| bot_mem => exact ⟨isOpen_empty, .empty⟩
| top_mem => exact ⟨isOpen_univ, .univ⟩
| sdiff U hU V hV =>
Expand All @@ -365,7 +366,7 @@ lemma IsConstructible.induction_of_isTopologicalBasis {ι : Type*} [Nonempty ι]
(sdiff _ _ ht)
(ih ⟨isOpen_biUnion fun _ _ ↦ basis.isOpen ⟨_, rfl⟩, .biUnion hs
fun i _ ↦ basis.isRetrocompact compact_inter _⟩)
| sup' s _ t _ hs' ht' => exact union _ _ _ _ hs' ht'
| sup s _ t _ hs' ht' => exact union _ _ _ _ hs' ht'

end CompactSpace

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