Theorems · Theorem · order theory
infClosed_countableInfClosure
∀ {α : Type u_2} {s : Set α} [inst : SemilatticeInf α], InfClosed (countableInfClosure s)- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 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.
Cites8
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
- SemilatticeInfstatement and proof · cited by 634
- ClosureOperatorstatement · cited by 371
- InfClosedstatement · cited by 57
- countableInfClosurestatement · cited by 21
- countableInfClosed_countableInfClosureproof · cited by 5
- CountableInfClosed.infClosedproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- inf_mem_countableInfClosureproof · cited by 0
- finsetInf'_mem_countableInfClosureproof · cited by 0