Theorems · Definition · order theory
countableSupClosure
{α : Type u_2} → [Preorder α] → ClosureOperator (Set α)Every set generates a set closed under countable supremum.
- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- Set.Nonemptyproof · cited by 2,627
- Set.Countableproof · cited by 545
- ClosureOperatorstatement · cited by 371
- IsLUBproof · cited by 280
- CountableSupClosedproof · cited by 27
- ClosureOperator.ofPredproof · cited by 4
Cited by21
Results whose statement or proof uses this declaration.
- subset_countableSupClosurestatement and proof · cited by 7
- countableSupClosed_countableSupClosurestatement and proof · cited by 5
- countableSupClosure_minstatement · cited by 3
- supClosed_countableSupClosurestatement · cited by 2
- countableSupClosure_eq_selfstatement and proof · cited by 1
- mem_countableSupClosure_iffstatement · cited by 1
- mem_countableSupClosure_iff_iSupstatement and proof · cited by 1
- upperBounds_countableSupClosurestatement and proof · cited by 1
- CountableSupClosed.countableSupClosure_eqstatement · cited by 0
- iSup_mem_countableSupClosurestatement · cited by 0
- isLUB_countableSupClosurestatement · cited by 0
- InfClosed.countableSupClosurestatement and proof · cited by 0