Theorems · Theorem · order theory
eq_top_iff
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, a = ⊤ ↔ ⊤ ≤ a- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 236 results in Mathlib
- Foundations
- Depth 9 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.
Cites4
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
- top_le_iffproof · cited by 175
Cited by236
Results whose statement or proof uses this declaration.
- Module.Basis.span_eqproof · cited by 44
- Module.Finite.of_surjectiveproof · cited by 29
- Submodule.eq_top_iff'proof · cited by 24
- Subgroup.eq_top_iff'proof · cited by 13
- Module.Finite.of_restrictScalars_finiteproof · cited by 12
- AddSubgroup.eq_top_iff'proof · cited by 11
- Ideal.map_isPrime_of_surjectiveproof · cited by 11
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- Ideal.span_singleton_eq_topproof · cited by 10
- Set.centralizer_eq_top_iff_subsetproof · cited by 8
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- Subgroup.map_top_of_surjectiveproof · cited by 7
Showing the 200 most cited of 236.