Theorems · Theorem · order theory
BooleanSubalgebra.iSup_mem
∀ {ι : Sort u_1} {α : Type u_2} [inst : CompleteBooleanAlgebra α] {L : BooleanSubalgebra α} {f : ι → α} [Finite ι],
(∀ (i : ι), f i ∈ L) → ⨆ i, f i ∈ L- Defined in
- Mathlib.Order.BooleanSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteBooleanAlgebraFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- BooleanSubalgebrastatement and proof · cited by 104
- CompleteBooleanAlgebrastatement and proof · cited by 32
- BooleanSubalgebra.supClosedproof · cited by 7
- BooleanSubalgebra.bot_memproof · cited by 7
- SupClosed.iSup_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsConstructible.iUnionproof · cited by 0