Theorems · Theorem · order theory
le_partialSups
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
(f : ι → α), f ≤ ⇑(partialSups f)- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 75 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
- le_rflproof · cited by 1,558
- OrderHomstatement · cited by 934
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
- le_partialSups_of_leproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Monotone.partialSups_eqproof · cited by 7
- ciSup_partialSups_eqproof · cited by 2
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- disjointed_partialSupsproof · cited by 1
- partialSups_add_one_eq_sup_disjointedproof · cited by 0