Theorems · Theorem · order theory
disjoint_partialSups_left
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι] [inst_2 : DistribLattice α]
[inst_3 : OrderBot α] {f : ι → α} {i : ι} {x : α}, Disjoint ((partialSups f) i) x ↔ ∀ j ≤ i, Disjoint (f j) x- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Disjointstatement and proof · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- OrderHomstatement · cited by 934
- LocallyFiniteOrderBotstatement and proof · cited by 286
- DistribLatticestatement and proof · cited by 150
- partialSupsstatement · cited by 67
- disjoint_sup_leftproof · cited by 4
- partialSups_iff_forallproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- partialSups_disjoint_of_disjointproof · cited by 0