Theorems · Theorem · order theory
countableInfClosure_eq_self
∀ {α : Type u_2} {s : Set α} [inst : Preorder α], countableInfClosure s = s ↔ CountableInfClosed s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- ClosureOperatorstatement · cited by 371
- CountableInfClosedstatement · cited by 27
- countableInfClosurestatement and proof · cited by 21
- ClosureOperator.isClosed_iffproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- CountableInfClosed.countableInfClosure_eqproof · cited by 0
- countableInfClosure_univproof · cited by 0
- countableInfClosure_singletonproof · cited by 0
- countableInfClosure_emptyproof · cited by 0