Theorems · Theorem · order theory
OrderIso.map_ciSup_set
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : ConditionallyCompleteLattice α]
[inst_1 : ConditionallyCompleteLattice β] (e : α ≃o β) {s : Set γ} {f : γ → α},
BddAbove (f '' s) → s.Nonempty → e (⨆ i, f ↑i) = ⨆ i, e (f ↑i)- Cited by
- 1 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- 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_ciSup_setproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- OrderIso.map_ciInf_setproof · cited by 0