Theorems · Theorem · order theory
Directed.Iic_ciInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderInf α] [Nonempty ι] {f : ι → α},
Directed (fun x1 x2 => x2 ≤ x1) f → BddBelow (Set.range f) → Set.Iic (⨅ i, f i) = ⋂ i, Set.Iic (f i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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Cites12
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
- Set.extproof · cited by 2,266
- iInfstatement · cited by 1,690
- Set.Iicstatement · cited by 1,111
- Set.iInterstatement · cited by 1,084
- BddBelowstatement and proof · cited by 401
- Directedstatement and proof · cited by 213
- Set.mem_iInterproof · cited by 69
- ConditionallyCompletePartialOrderInfstatement and proof · cited by 51
- Set.mem_Iicproof · cited by 37
- Directed.le_ciInf_iffproof · cited by 2
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