Theorems · Theorem · order theory
partialSups_apply
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
(f : ι → α) (i : ι), (partialSups f) i = (Finset.Iic i).sup' ⋯ f- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- 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
- Finset.Iicstatement · cited by 280
- Finset.sup'statement · cited by 174
- partialSupsstatement · cited by 67
- Finset.nonempty_Iicstatement · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- partialSups_disjointedproof · cited by 5
- partialSups_iff_forallproof · cited by 3
- disjointed_succproof · cited by 3
- Finset.disjiUnion_Iic_disjointedproof · cited by 2
- Monotone.disjointed_succ_supproof · cited by 1
- Fintype.sup_disjointedproof · cited by 1
- disjointed_partialSupsproof · cited by 1