Theorems · Theorem · order theory
Disjoint.le_bot
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {a b : α}, Disjoint a b → a ⊓ b ≤ ⊥- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SemilatticeInfOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Disjointstatement · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- SemilatticeInfstatement and proof · cited by 634
- disjoint_iff_inf_leproof · cited by 64
Cited by52
Results whose statement or proof uses this declaration.
- Disjoint.eq_botproof · cited by 52
- Disjoint.preimageproof · cited by 22
- Metric.closedBall_sdiff_ballproof · cited by 10
- BoxIntegral.Prepartition.eq_of_mem_of_memproof · cited by 6
- normal_exists_closure_subsetproof · cited by 5
- Set.indicator_union_of_disjointproof · cited by 5
- Disjoint.left_le_of_le_sup_rightproof · cited by 4
- Set.injOn_unionproof · cited by 3
- BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_rightproof · cited by 3
- ProperlyDiscontinuousSMul.exists_nhds_image_smul_eq_selfproof · cited by 3
- Set.mulIndicator_union_of_disjointproof · cited by 3
- ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_selfproof · cited by 3