Theorems · Definition · order theory
BooleanSubalgebra.closure
{α : Type u_2} → [inst : BooleanAlgebra α] → Set α → BooleanSubalgebra αThe minimum Boolean subalgebra containing a given set.
- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- InfSet.sInfproof · cited by 935
- BooleanAlgebrastatement and proof · cited by 300
- BooleanSubalgebrastatement and proof · cited by 104
Cited by13
Results whose statement or proof uses this declaration.
- Topology.IsConstructibleproof · cited by 45
- BooleanSubalgebra.subset_closurestatement · cited by 9
- Topology.IsConstructible.empty_union_inductionproof · cited by 3
- BooleanSubalgebra.closure_bot_sup_inductionstatement and proof · cited by 2
- BooleanSubalgebra.closure_lestatement · cited by 2
- BooleanSubalgebra.mem_closurestatement · cited by 1
- BooleanSubalgebra.mem_closure_iff_sup_sdiffstatement and proof · cited by 1
- Topology.IsConstructible.induction_of_isTopologicalBasisproof · cited by 1
- BooleanSubalgebra.latticeClosure_subset_closurestatement and proof · cited by 1
- BooleanSubalgebra.closure_monostatement · cited by 1
- BooleanSubalgebra.closure_sdiff_sup_inductionstatement and proof · cited by 1
- BooleanSubalgebra.mem_closure_of_memstatement · cited by 0