Theorems · Theorem · order theory
disjoint_iff_inf_le
∀ {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
- 64 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SemilatticeInfOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- LE.le.transproof · cited by 3,151
- Disjointstatement and proof · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- SemilatticeInfstatement and proof · cited by 634
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- le_infproof · cited by 107
Cited by64
Results whose statement or proof uses this declaration.
- Set.disjoint_leftproof · cited by 121
- disjoint_iffproof · cited by 76
- Disjoint.le_botproof · cited by 52
- Set.disjoint_iffproof · cited by 27
- disjoint_sdiff_self_rightproof · cited by 22
- Disjoint.preimageproof · cited by 22
- disjoint_sdiff_self_leftproof · cited by 21
- Submodule.disjoint_defproof · cited by 21
- disjoint_compl_leftproof · cited by 17
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- le_compl_iff_disjoint_rightproof · cited by 10
- disjoint_sdiff_sdiffproof · cited by 6