Theorems · Theorem · order theory
le_sSup
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s : Set α} {a : α}, a ∈ s → a ≤ sSup s- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeSup
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.
- Setstatement and proof · cited by 53,352
- SupSet.sSupstatement · cited by 954
- isLUB_sSupproof · cited by 21
- CompleteSemilatticeSupstatement and proof · cited by 18
Cited by79
Results whose statement or proof uses this declaration.
- le_iSupproof · cited by 207
- sSup_eq_iSupproof · cited by 42
- Set.subset_sUnion_of_memproof · cited by 39
- Ideal.radical_eq_sInfproof · cited by 21
- nhds_le_nhdsSetproof · cited by 8
- sSup_eq_botproof · cited by 7
- Order.krullDim_orderDualproof · cited by 7
- Order.krullDim_le_of_strictMonoproof · cited by 6
- Ideal.exists_le_prime_disjointproof · cited by 5
- Filter.HasBasis.limsSup_eq_iInf_sSupproof · cited by 5
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- MeasureTheory.Submartingale.ae_tendsto_limitProcessproof · cited by 4