Theorems · Theorem · combinatorics
upperClosure_sups
∀ {α : Type u_2} [inst : SemilatticeSup α] (s t : Set α), upperClosure (s ⊻ t) = upperClosure s ⊔ upperClosure t- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coeproof · cited by 8,199
- LE.le.transproof · cited by 3,151
- Set.extproof · cited by 2,266
- SemilatticeSupstatement and proof · cited by 785
- le_sup_leftproof · cited by 265
- UpperSetstatement · cited by 245
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- HasSups.supsstatement · cited by 103
- upperClosurestatement and proof · cited by 84
- Set.hasSupsstatement · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- Finset.truncatedInf_sups_of_notMemproof · cited by 1