Theorems · Theorem · order theory
BooleanSubalgebra.subset_closure
∀ {α : Type u_2} [inst : BooleanAlgebra α] {s : Set α}, s ⊆ ↑(BooleanSubalgebra.closure s)- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 64 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.coestatement and proof · cited by 8,199
- BooleanAlgebrastatement and proof · cited by 300
- BooleanSubalgebrastatement and proof · cited by 104
- BooleanSubalgebra.closurestatement · cited by 12
- BooleanSubalgebra.mem_closureproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- IsRetrocompact.isConstructibleproof · cited by 7
- Topology.IsConstructible.empty_union_inductionstatement and proof · cited by 3
- BooleanSubalgebra.closure_bot_sup_inductionstatement and proof · cited by 2
- BooleanSubalgebra.closure_leproof · cited by 2
- BooleanSubalgebra.mem_closure_iff_sup_sdiffproof · cited by 1
- Topology.IsConstructible.induction_of_isTopologicalBasisproof · cited by 1
- BooleanSubalgebra.latticeClosure_subset_closureproof · cited by 1
- BooleanSubalgebra.closure_sdiff_sup_inductionstatement and proof · cited by 1
- BooleanSubalgebra.mem_closure_of_memproof · cited by 0