Theorems · Theorem · order theory
disjoint_top
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : BoundedOrder α] {a : α}, Disjoint a ⊤ ↔ a = ⊥- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrderBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- Disjointstatement and proof · cited by 2,201
- le_rflproof · cited by 1,558
- le_topproof · cited by 411
- LE.le.trans_eqproof · cited by 328
- BoundedOrderstatement and proof · cited by 270
- bot_uniqueproof · cited by 57
Cited by5
Results whose statement or proof uses this declaration.
- compl_topproof · cited by 4
- Set.disjoint_univproof · cited by 1
- hasEigenvalue_toLin_diagonal_iffproof · cited by 1
- Subgroup.comap_eq_ker_of_surjectiveproof · cited by 1
- AddSubgroup.comap_eq_ker_of_surjectiveproof · cited by 0