Theorems · Theorem · order theory
iSup_partialSups_eq
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι] [inst_2 : CompleteLattice α]
(f : ι → α), ⨆ i, (partialSups f) i = ⨆ i, f iVersion of ciSup_partialSups_eq without boundedness assumptions, but requiring a
CompleteLattice rather than just a ConditionallyCompleteLattice.
- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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
- Set.rangeproof · cited by 4,705
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- OrderHomstatement · cited by 934
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
- OrderTop.bddAboveproof · cited by 16
- ciSup_partialSups_eqproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.isSigmaSubadditive_of_addContent_iUnion_eq_tsumproof · cited by 2
- iSup_eq_iSup_of_partialSups_eq_partialSupsproof · cited by 1
- iSup_le_iSup_of_partialSups_le_partialSupsproof · cited by 0