Theorems · Theorem · order theory
CountableInfClosed.infClosed
∀ {α : Type u_2} {s : Set α} [inst : SemilatticeInf α], CountableInfClosed s → InfClosed s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
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
- SemilatticeInfstatement and proof · cited by 634
- InfClosedstatement · cited by 57
- CountableInfClosedstatement and proof · cited by 27
- Set.countable_singletonproof · cited by 13
- Set.insert_nonemptyproof · cited by 13
- CountableInfClosed.isGLB_memproof · cited by 10
- isGLB_pairproof · cited by 5
- Set.countable_insertproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- infClosed_countableInfClosureproof · cited by 2
- CountableInfClosed.finsetInf'_memproof · cited by 1
- CountableInfClosed.directedOnproof · cited by 0