Theorems · Theorem · order theory
disjoint_comm
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α] {a b : α}, Disjoint a b ↔ Disjoint b a- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Disjointstatement · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
Cited by49
Results whose statement or proof uses this declaration.
- Disjoint.symmproof · cited by 125
- Set.disjoint_rightproof · cited by 17
- Set.disjoint_singleton_rightproof · cited by 17
- Finset.disjoint_singleton_rightproof · cited by 12
- Finset.disjoint_rightproof · cited by 9
- le_compl_iff_disjoint_leftproof · cited by 7
- Finset.disjoint_insert_rightproof · cited by 6
- Matroid.delete_eq_self_iffproof · cited by 4
- Matroid.Indep.contract_dep_iffproof · cited by 4
- Matroid.IsBasis'.contract_indep_iffproof · cited by 4
- sdiff_eq_self_iff_disjointproof · cited by 4
- Filter.disjoint_principal_leftproof · cited by 4