Theorems · Theorem · order theory
IsCompactlyGenerated.BooleanGenerators.atomistic
∀ {α : Type u_1} [inst : CompleteLattice α] {S : Set α} [IsCompactlyGenerated α],
IsCompactlyGenerated.BooleanGenerators S → ∀ a ≤ sSup S, ∃ T ⊆ S, a = sSup T- Defined in
- Mathlib.Order.BooleanGenerators
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · 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
- Finset.supproof · cited by 530
- Set.Subset.transproof · cited by 218
- le_sSupproof · cited by 79
- IsCompactlyGeneratedstatement and proof · cited by 37
Cited by4
Results whose statement or proof uses this declaration.
- IsCompactlyGenerated.BooleanGenerators.mem_of_isAtom_of_le_sSup_atomsproof · cited by 3
- IsCompactlyGenerated.BooleanGenerators.isAtomistic_of_sSup_eq_topproof · cited by 1
- IsCompactlyGenerated.BooleanGenerators.eq_atoms_of_sSup_eq_topproof · cited by 0
- IsCompactlyGenerated.BooleanGenerators.sSup_interproof · cited by 0