Theorems · Definition · order theory

IsCompactlyGenerated.BooleanGenerators.booleanAlgebraOfSSupEqTop

{α : Type u_1} →
  [inst : CompleteLattice α] →
    {S : Set α} → [IsCompactlyGenerated α] → IsCompactlyGenerated.BooleanGenerators S → sSup S = ⊤ → BooleanAlgebra α

A compactly generated complete lattice generated by Boolean generators is a Boolean algebra.

Defined in: Mathlib.Order.BooleanGenerators
Cited by: 0 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompleteLattice IsCompactlyGenerated

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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
BooleanAlgebrastatement · cited by 300
DistribLatticeproof · cited by 150
IsCompactlyGeneratedstatement and proof · cited by 37
ComplementedLatticeproof · cited by 30
IsCompactlyGenerated.BooleanGeneratorsstatement and proof · cited by 11
IsCompactlyGenerated.BooleanGenerators.distribLatticeOfSSupEqTopproof · cited by 1
DistribLattice.booleanAlgebraOfComplementedproof · cited by 0
IsCompactlyGenerated.BooleanGenerators.complementedLattice_of_sSup_eq_topproof · cited by 0

Cited by1

Results whose statement or proof uses this declaration.

IsCompactlyGenerated.BooleanGenerators.booleanAlgebra_of_sSup_eq_topproof · cited by 0