IsCompactlyGenerated.BooleanGenerators.booleanAlgebra_of_sSup_eq_top

Deprecated since 2026-07-18Use IsCompactlyGenerated.BooleanGenerators.booleanAlgebraOfSSupEqTop instead.

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

Alias of IsCompactlyGenerated.BooleanGenerators.booleanAlgebraOfSSupEqTop. 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 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompleteLattice IsCompactlyGenerated

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Setstatement · cited by 53,352
Top.topstatement · cited by 9,680
CompleteLatticestatement · cited by 1,048
SupSet.sSupstatement · cited by 954
BooleanAlgebrastatement · cited by 300
IsCompactlyGeneratedstatement · cited by 37
IsCompactlyGenerated.BooleanGeneratorsstatement · cited by 11
IsCompactlyGenerated.BooleanGenerators.booleanAlgebraOfSSupEqTopproof · cited by 0

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