Theorems · Theorem · combinatorics
Set.sups_subset_self
∀ {α : Type u_2} [inst : SemilatticeSup α] {s : Set α}, s ⊻ s ⊆ s ↔ SupClosed s- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- 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
- SemilatticeSupstatement and proof · cited by 785
- HasSups.supsstatement · cited by 103
- SupClosedstatement · cited by 57
- Set.hasSupsstatement · cited by 43
- Set.sups_subset_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Set.sups_eq_selfproof · cited by 0