Theorems · Theorem · order theory
disjoint_bot_left
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, Disjoint ⊥ a- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 8 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.
Cites4
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 · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
Cited by8
Results whose statement or proof uses this declaration.
- Set.empty_disjointproof · cited by 2
- Finset.empty_disjUnionstatement · cited by 1
- Pairwise.disjoint_extend_botproof · cited by 1
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- Set.intersecting_iff_pairwise_not_disjointproof · cited by 1
- Set.Intersecting.bot_notMemproof · cited by 1
- Finset.disjoint_empty_leftproof · cited by 0
- Multiset.zero_disjointproof · cited by 0