Theorems · Definition · order theory
infClosure
{α : Type u_3} → [SemilatticeInf α] → ClosureOperator (Set α)Every set in a meet-semilattice generates a set closed under meet.
- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 69 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.
Cites10
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Finset.Nonemptyproof · cited by 1,001
- SemilatticeInfstatement and proof · cited by 634
- ClosureOperatorstatement · cited by 371
- Finset.inf'proof · cited by 117
- InfClosedproof · cited by 57
- ClosureOperator.ofPredproof · cited by 4
Cited by21
Results whose statement or proof uses this declaration.
- subset_infClosurestatement and proof · cited by 6
- infClosed_infClosurestatement and proof · cited by 5
- infClosure_eq_selfstatement and proof · cited by 4
- infClosure_minstatement · cited by 3
- supClosure_infClosurestatement · cited by 2
- infClosure_prodstatement and proof · cited by 1
- SupClosed.infClosurestatement and proof · cited by 1
- lowerBounds_infClosurestatement and proof · cited by 1
- Set.Finite.infClosurestatement and proof · cited by 1
- finsetInf'_mem_infClosurestatement · cited by 1
- inf_mem_infClosurestatement · cited by 0
- latticeClosure_prodproof · cited by 0