Theorems · Theorem · order theory
IsLUB.sSup_eq
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s : Set α} {a : α}, IsLUB s a → sSup s = aAlias of the forward direction of isLUB_iff_sSup_eq.
- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 10 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
- IsLUBstatement · cited by 280
- CompleteSemilatticeSupstatement and proof · cited by 18
- isLUB_iff_sSup_eqproof · cited by 3
Cited by17
Results whose statement or proof uses this declaration.
- sSup_emptyproof · cited by 19
- sSup_singletonproof · cited by 14
- sSup_pairproof · cited by 11
- sSup_unionproof · cited by 5
- sSup_image2_eq_sSup_sSupproof · cited by 5
- sSup_insertproof · cited by 4
- himp_eq_sSupproof · cited by 2
- sSup_atoms_eq_topproof · cited by 2
- LeftOrdContinuous.map_sSup'proof · cited by 2
- scottContinuous_iff_map_sSupproof · cited by 2
- sSup_univproof · cited by 1
- compl_eq_sSup_disjointproof · cited by 1