Theorems · Theorem · order theory
top_unique
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, ⊤ ≤ a → a = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 102 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- PartialOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LE.le.antisymmproof · cited by 507
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
Cited by102
Results whose statement or proof uses this declaration.
- Filter.principal_univproof · cited by 46
- Codisjoint.eq_topproof · cited by 22
- iInf_topproof · cited by 21
- eq_top_monoproof · cited by 12
- dimH_monoproof · cited by 8
- ENNReal.eq_top_of_forall_nnreal_leproof · cited by 7
- separableClosure.eq_top_iffproof · cited by 6
- MeasureTheory.Measure.count_apply_infiniteproof · cited by 5
- Ideal.sup_iInf_eq_topproof · cited by 5
- MeasureTheory.OuterMeasure.top_applyproof · cited by 5
- CompactSpace.elim_nhds_subcoverproof · cited by 5
- ENNReal.tsum_eq_top_of_eq_topproof · cited by 5