Theorems · Definition · combinatorics
Set.hasSups
{α : Type u_2} → [SemilatticeSup α] → HasSups (Set α)s ⊻ t is the set of elements of the form a ⊔ b where a ∈ s, b ∈ t.
- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
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
- SemilatticeSupstatement and proof · cited by 785
- Set.image2proof · cited by 311
- HasSupsstatement · cited by 1
Cited by43
Results whose statement or proof uses this declaration.
- Finset.coe_supsstatement · cited by 3
- Set.sups_subset_iffstatement · cited by 1
- Set.sups_subset_selfstatement · cited by 1
- Set.mem_supsstatement · cited by 1
- upperClosure_supsstatement · cited by 1
- Set.subset_sups_selfstatement · cited by 1
- Set.sep_sups_lestatement · cited by 1
- Set.infs_sups_subset_rightstatement · cited by 0
- Set.sups_assocstatement · cited by 0
- Set.sups_commstatement · cited by 0
- Set.sups_emptystatement · cited by 0
- Set.sups_eq_emptystatement · cited by 0