Theorems · Theorem · order theory
BooleanSubalgebra.biSup_mem
∀ {α : Type u_2} [inst : CompleteBooleanAlgebra α] {L : BooleanSubalgebra α} {ι : Type u_5} {t : Set ι} {f : ι → α},
t.Finite → (∀ i ∈ t, f i ∈ L) → ⨆ i ∈ t, f i ∈ 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.
Cites8
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
- iSupstatement · cited by 2,415
- Set.Finitestatement and proof · cited by 1,814
- BooleanSubalgebrastatement and proof · cited by 104
- CompleteBooleanAlgebrastatement and proof · cited by 32
- BooleanSubalgebra.supClosedproof · cited by 7
- BooleanSubalgebra.bot_memproof · cited by 7
- SupClosed.biSup_memproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsConstructible.biUnionproof · cited by 3