Theorems · Theorem · order theory
IsCompactlyGenerated.BooleanGenerators.eq_atoms_of_sSup_eq_top
∀ {α : Type u_1} [inst : CompleteLattice α] {S : Set α} [IsCompactlyGenerated α],
IsCompactlyGenerated.BooleanGenerators S → sSup S = ⊤ → S = {a | IsAtom a}- Defined in
- Mathlib.Order.BooleanGenerators
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- le_topproof · cited by 411
- Eq.geproof · cited by 375
- IsAtomstatement and proof · cited by 130
- IsCompactlyGeneratedstatement and proof · cited by 37
- sSup_le_sSupproof · cited by 24
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