Theorems · Theorem · order theory
top_le_iff
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, ⊤ ≤ a ↔ a = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 175 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 15 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 · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- LE.le.ge_iff_eqproof · cited by 12
Cited by175
Results whose statement or proof uses this declaration.
- eq_top_iffproof · cited by 236
- codisjoint_iffproof · cited by 53
- Set.univ_subset_iffproof · cited by 49
- CategoryTheory.GrothendieckTopology.superset_coveringproof · cited by 37
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- inf_eq_top_iffproof · cited by 7
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- MvPowerSeries.le_weightedOrderproof · cited by 7
- Module.FinitePresentation.fg_kerproof · cited by 6
- himp_selfproof · cited by 6
- EReal.toENNReal_of_nonposproof · cited by 5
- sInf_eq_topproof · cited by 5