Theorems · Theorem · order theory
sSup_singleton
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {a : α}, sSup {a} = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 11 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 · cited by 53,352
- SupSet.sSupstatement · cited by 954
- CompleteSemilatticeSupstatement and proof · cited by 18
- IsLUB.sSup_eqproof · cited by 17
- isLUB_singletonproof · cited by 10
Cited by14
Results whose statement or proof uses this declaration.
- nhdsSet_singletonproof · cited by 19
- Set.sUnion_singletonproof · cited by 17
- iSup_constproof · cited by 13
- TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducibleproof · cited by 2
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2
- Partition.top_defstatement · cited by 1
- Submodule.restrictScalars_supproof · cited by 1
- CompleteLattice.isCompactlyGenerated_of_wellFoundedGTproof · cited by 0
- Partition.parts_topproof · cited by 0
- sSup_oneproof · cited by 0
- sSupIndep_pairproof · cited by 0
- Partition.mem_top_iffproof · cited by 0