Theorems · Theorem · order theory
ciSup_partialSups_eq
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι]
[inst_2 : ConditionallyCompleteLattice α] {f : ι → α}, BddAbove (Set.range f) → ⨆ i, (partialSups f) i = ⨆ i, f i- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.Elemproof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- Set.Iicproof · cited by 1,111
- OrderHomstatement · cited by 934
- BddAbovestatement and proof · cited by 620
- LE.le.antisymmproof · cited by 507
- ConditionallyCompleteLatticestatement and proof · cited by 364
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
Cited by2
Results whose statement or proof uses this declaration.
- iSup_partialSups_eqproof · cited by 3
- ciSup_partialSups_eq'proof · cited by 0