Theorems · Theorem · order theory
disjoint_self
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, Disjoint a a ↔ a = ⊥- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bot.botstatement and proof · cited by 4,720
- Disjointstatement and proof · cited by 2,201
- le_rflproof · cited by 1,558
- OrderBotstatement and proof · cited by 1,055
- LE.le.trans_eqproof · cited by 328
- bot_uniqueproof · cited by 57
Cited by28
Results whose statement or proof uses this declaration.
- Disjoint.neproof · cited by 5
- le_sdiff_rightproof · cited by 4
- jacobsonSpace_iff_locallyClosedproof · cited by 4
- summable_jacobiTheta₂_term_iffproof · cited by 4
- Set.Intersecting.insertproof · cited by 4
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- AddAction.IsFixedBlock.isBlockproof · cited by 3
- iSupIndep.injOnproof · cited by 3
- le_compl_selfproof · cited by 2
- LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdealproof · cited by 2
- Finpartition.exists_le_of_leproof · cited by 1
- AddAction.IsBlock.emptyproof · cited by 1