Theorems · Theorem · order theory
Set.finite_iff_bddAbove
∀ {α : Type u_3} {s : Set α} [inst : SemilatticeSup α] [LocallyFiniteOrder α] [OrderBot α], s.Finite ↔ BddAbove s- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Bot.botproof · cited by 4,720
- Set.Finitestatement and proof · cited by 1,814
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderstatement and proof · cited by 658
- BddAbovestatement and proof · cited by 620
- Finset.supproof · cited by 530
- Set.Finite.toFinsetproof · cited by 351
- bot_leproof · cited by 306
- Set.Finite.subsetproof · cited by 285
- upperBoundsproof · cited by 263
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.existsMaximalSubsetProperty_of_bddproof · cited by 0