Theorems · Theorem · order theory
SupClosed.countableInfClosure
∀ {α : Type u_2} {s : Set α} [inst : Order.Coframe α], SupClosed s → SupClosed (countableInfClosure s)If a set is closed under binary suprema, then its countable infimum closure is also closed under binary suprema.
- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- iInfproof · cited by 1,690
- ClosureOperatorstatement · cited by 371
- Nat.unpairproof · cited by 67
- SupClosedstatement and proof · cited by 57
- Order.Coframestatement and proof · cited by 38
- countableInfClosurestatement and proof · cited by 21
- iInf_sup_iInfproof · cited by 3
- iInf_unpairproof · cited by 3
- iInf_prod'proof · cited by 2
- mem_countableInfClosure_iff_iInfproof · cited by 1
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