Theorems · Theorem · order theory
Disjoint.left_le_of_le_sup_right
∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : OrderBot α] {a b c : α}, a ≤ b ⊔ c → Disjoint a c → a ≤ b- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- DistribLatticeOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Disjointstatement and proof · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- le_transproof · cited by 985
- bot_leproof · cited by 306
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- DistribLatticestatement and proof · cited by 150
- Disjoint.le_botproof · cited by 52
- le_of_inf_le_sup_leproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- connectedComponent_eq_iInter_isClopenproof · cited by 2
- Codisjoint.left_le_of_le_inf_rightproof · cited by 2
- Disjoint.left_le_of_le_sup_leftproof · cited by 2
- Disjoint.subset_left_of_subset_unionproof · cited by 2