Theorems · Definition · order theory
supClosure
{α : Type u_3} → [SemilatticeSup α] → ClosureOperator (Set α)Every set in a join-semilattice generates a set closed under join.
- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSup
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
- SemilatticeSupstatement and proof · cited by 785
- ClosureOperatorstatement · cited by 371
- Finset.sup'proof · cited by 174
- SupClosedproof · cited by 57
- ClosureOperator.ofPredproof · cited by 4
Cited by34
Results whose statement or proof uses this declaration.
- subset_supClosurestatement and proof · cited by 11
- supClosed_supClosurestatement and proof · cited by 8
- MeasureTheory.AddContent.supClosurestatement · cited by 5
- MeasureTheory.IsSetSemiring.isSetRing_supClosurestatement and proof · cited by 3
- supClosure_minstatement · cited by 3
- MeasureTheory.IsSetSemiring.mem_supClosure_iffstatement and proof · cited by 2
- measurableSet_generateFrom_of_mem_supClosurestatement and proof · cited by 2
- MeasureTheory.IsSetSemiring.sdiff_mem_supClosurestatement · cited by 2
- supClosure_infClosurestatement · cited by 2
- MeasureTheory.AddContent.supClosure_apply_of_memstatement · cited by 2
- upperBounds_supClosurestatement and proof · cited by 1
- Set.Finite.supClosurestatement and proof · cited by 1