Theorems · Definition · order theory
CompleteLattice.IsSupFiniteCompact
(α : Type u_2) → [CompleteLattice α] → Prop
A compactness property for a complete lattice is that any subset has a finite subset with the
same sSup.
- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Finset.supproof · cited by 530
Cited by10
Results whose statement or proof uses this declaration.
- isNoetherian_iff'proof · cited by 6
- CompleteLattice.wellFoundedGT_characterisationsstatement and proof · cited by 4
- CompleteLattice.isSupFiniteCompact_iff_all_elements_compactstatement and proof · cited by 3
- CompleteLattice.wellFoundedGT_iff_isSupFiniteCompactstatement and proof · cited by 3
- CompleteLattice.WellFoundedGT.isSupFiniteCompactstatement · cited by 2
- CompleteLattice.isSupClosedCompact_iff_wellFoundedGTproof · cited by 1
- CompleteLattice.isSupFiniteCompact_iff_isSupClosedCompactstatement and proof · cited by 1
- CompleteLattice.IsSupFiniteCompact.isSupClosedCompactstatement and proof · cited by 1
- CompleteLattice.IsSupClosedCompact.isSupFiniteCompactstatement · cited by 0
- CompleteLattice.IsSupFiniteCompact.wellFoundedGTstatement · cited by 0