Theorems · Theorem · combinatorics
Set.sups_eq_self
∀ {α : Type u_2} [inst : SemilatticeSup α] {s : Set α}, s ⊻ s = s ↔ SupClosed s- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 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.
Cites8
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
- LE.le.ge_iff_eq'proof · cited by 50
- Set.hasSupsstatement · cited by 43
- Set.subset_sups_selfproof · cited by 1
- Set.sups_subset_selfproof · cited by 1
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