Theorems · Theorem · order theory
IsCompactlyGenerated.BooleanGenerators.complementedLattice_of_sSup_eq_top
∀ {α : Type u_1} [inst : CompleteLattice α] {S : Set α} [IsCompactlyGenerated α],
IsCompactlyGenerated.BooleanGenerators S → sSup S = ⊤ → ComplementedLattice α- Defined in
- Mathlib.Order.BooleanGenerators
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- DistribLatticeproof · cited by 150
- IsCompactlyGeneratedstatement and proof · cited by 37
- ComplementedLatticestatement · cited by 30
- IsAtomisticproof · cited by 18
- IsCompactlyGenerated.BooleanGeneratorsstatement and proof · cited by 11
- complementedLattice_of_isAtomisticproof · cited by 2
- IsCompactlyGenerated.BooleanGenerators.distribLatticeOfSSupEqTopproof · cited by 1
- IsCompactlyGenerated.BooleanGenerators.isAtomistic_of_sSup_eq_topproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsCompactlyGenerated.BooleanGenerators.booleanAlgebraOfSSupEqTopproof · cited by 0