Theorems · Theorem · combinatorics
Set.sups_nonempty
∀ {α : Type u_2} [inst : SemilatticeSup α] {s t : Set α}, (s ⊻ t).Nonempty ↔ s.Nonempty ∧ t.Nonempty- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.Nonemptystatement · cited by 2,627
- SemilatticeSupstatement and proof · cited by 785
- HasSups.supsstatement · cited by 103
- Set.hasSupsstatement · cited by 43
- Set.image2_nonempty_iffproof · cited by 14
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.