Theorems · Theorem · order theory
Directed.Ici_ciSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α] [Nonempty ι] {f : ι → α},
Directed (fun x1 x2 => x1 ≤ x2) f → BddAbove (Set.range f) → Set.Ici (⨆ i, f i) = ⋂ i, Set.Ici (f i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- Set.extproof · cited by 2,266
- Set.iInterstatement · cited by 1,084
- Set.Icistatement · cited by 1,070
- BddAbovestatement and proof · cited by 620
- Directedstatement and proof · cited by 213
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- Directed.ciSup_le_iffproof · cited by 2
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