Theorems · Theorem · order theory
le_sSup_iff
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s : Set α} {a : α}, a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 1 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.
Cites7
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
- le_transproof · cited by 985
- SupSet.sSupstatement and proof · cited by 954
- upperBoundsstatement and proof · cited by 263
- le_sSupproof · cited by 79
- sSup_leproof · cited by 35
- CompleteSemilatticeSupstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- DedekindCut.factorEmbedding_principalproof · cited by 1