Theorems · Theorem · order theory
OrderIso.map_ciSup_of_directed
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α]
[inst_1 : ConditionallyCompletePartialOrderSup β] [Nonempty ι] (e : α ≃o β) {f : ι → α},
Directed (fun x1 x2 => x1 ≤ x2) f → BddAbove (Set.range f) → e (⨆ i, f i) = ⨆ i, e (f i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Directedstatement and proof · cited by 213
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- OrderIso.to_galoisConnectionproof · cited by 32
- GaloisConnection.l_ciSup_of_directedproof · cited by 2
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