Theorems · Theorem · order theory
PartialOrder.dirSupClosed_singleton
∀ {α : Type u_1} [inst : PartialOrder α] (a : α), DirSupClosed {a}- Defined in
- Mathlib.Order.DirSupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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
- PartialOrderstatement and proof · cited by 6,410
- Set.Nonemptyproof · cited by 2,627
- IsLUBproof · cited by 280
- DirectedOnproof · cited by 271
- DirSupClosedstatement · cited by 31
- IsLUB.uniqueproof · cited by 21
- isLUB_singletonproof · cited by 10
- Set.Nonempty.subset_singleton_iffproof · cited by 5
- Set.mem_singleton_of_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PartialOrder.dirSupClosedOn_singletonproof · cited by 0