Theorems · Theorem · combinatorics
Set.intersecting_iff_pairwise_not_disjoint
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {s : Set α},
s.Intersecting ↔ (s.Pairwise fun a b => ¬Disjoint a b) ∧ s ≠ {⊥}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInfOrderBot
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
- Bot.botstatement and proof · cited by 4,720
- Disjointstatement and proof · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- SemilatticeInfstatement and proof · cited by 634
- Set.Pairwisestatement and proof · cited by 321
- not_ne_iffproof · cited by 30
- disjoint_selfproof · cited by 28
- Set.Intersectingstatement and proof · cited by 22
- Set.eq_singleton_iff_unique_memproof · cited by 20
- Set.Pairwise.eqproof · cited by 12
- disjoint_bot_leftproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Set.Subsingleton.intersectingproof · cited by 1