Theorems · Theorem · order theory
BooleanSubalgebra.sInf_mem
∀ {α : Type u_2} [inst : CompleteBooleanAlgebra α] {L : BooleanSubalgebra α} {s : Set α}, s.Finite → s ⊆ ↑L → sInf s ∈ L- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteBooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Finitestatement and proof · cited by 1,814
- InfSet.sInfstatement · cited by 935
- BooleanSubalgebrastatement and proof · cited by 104
- CompleteBooleanAlgebrastatement and proof · cited by 32
- BooleanSubalgebra.infClosedproof · cited by 7
- BooleanSubalgebra.top_memproof · cited by 5
- InfClosed.sInf_memproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsConstructible.sInterproof · cited by 0