Theorems · Theorem · order theory
partialSups_le_iff
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
{f : ι → α} {i : ι} {a : α}, (partialSups f) i ≤ a ↔ ∀ j ≤ i, f j ≤ a- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 3 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.
Cites8
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
- OrderHomstatement · cited by 934
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
- sup_le_iffproof · cited by 58
- partialSups_iff_forallproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- le_partialSups_of_leproof · cited by 4
- partialSups_leproof · cited by 3
- partialSups_monoproof · cited by 0