Theorems · Theorem · order theory
CompleteSemilatticeSup.isLUB_sSup
∀ {α : Type u_8} [self : CompleteSemilatticeSup α] (s : Set α), IsLUB s (sSup s)Every set has a least upper bound.
- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 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 · cited by 53,352
- SupSet.sSupstatement · cited by 954
- IsLUBstatement · cited by 280
- CompleteSemilatticeSupstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- isLUB_sSupproof · cited by 21