Theorems · Theorem · order theory
WithBot.denselyOrdered_set_iff_subsingleton
∀ {X : Type u_1} [inst : LinearOrder X] [LocallyFiniteOrder X] {s : Set (WithBot X)}, DenselyOrdered ↑s ↔ s.Subsingleton- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement and proof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Bot.botproof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- LT.lt.ne'proof · cited by 1,417
- LT.lt.neproof · cited by 872
- LT.lt.trans_leproof · cited by 678
- LocallyFiniteOrderstatement and proof · cited by 658
- WithBot.someproof · cited by 541
- DenselyOrderedstatement and proof · cited by 471
Cited by2
Results whose statement or proof uses this declaration.
- WithZero.denselyOrdered_set_iff_subsingletonproof · cited by 1
- WithTop.denselyOrdered_set_iff_subsingletonproof · cited by 0