Theorems · Theorem · order theory
OrderIso.map_ciSup
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α]
[inst_1 : ConditionallyCompleteLattice β] [Nonempty ι] (e : α ≃o β) {f : ι → α},
BddAbove (Set.range f) → e (⨆ i, f i) = ⨆ i, e (f i)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, 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
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- OrderIsostatement and proof · cited by 874
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- OrderIso.to_galoisConnectionproof · cited by 32
- GaloisConnection.l_ciSupproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- OrderIso.map_ciInfproof · cited by 4
- OrderIso.map_ciSup'proof · cited by 1
- ciSup_mulproof · cited by 1
- ciSup_addproof · cited by 1
- mul_ciSupproof · cited by 0
- add_ciSupproof · cited by 0