Theorems · Theorem · order theory
sSup_le_sSup
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s t : Set α}, s ⊆ t → sSup s ≤ sSup t- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 24 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.
Cites5
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
- IsLUB.monoproof · cited by 3
Cited by24
Results whose statement or proof uses this declaration.
- nhdsSet_monoproof · cited by 18
- CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSupproof · cited by 4
- inf_sSup_eq_iSup_inf_sup_finsetproof · cited by 4
- IsCompactlyGenerated.BooleanGenerators.atomisticproof · cited by 4
- sSupIndep.monoproof · cited by 4
- TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompactproof · cited by 3
- sSup_sdiff_singleton_botproof · cited by 2
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2
- le_iff_compact_le_impproof · cited by 2
- le_isotypicComponent_iffproof · cited by 2
- sSup_compact_le_eqproof · cited by 2
- CompleteLattice.WellFoundedGT.isSupFiniteCompactproof · cited by 2