Theorems · Theorem · order theory
DirSupClosedOn.iInter
∀ {α : Type u_1} {D : Set (Set α)} [inst : Preorder α] {ι : Sort u_2} {f : ι → Set α},
(∀ (i : ι), DirSupClosedOn D (f i)) → DirSupClosedOn D (⋂ i, f i)- Defined in
- Mathlib.Order.DirSupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.iInterstatement · cited by 1,084
- DirSupClosedOnstatement and proof · cited by 26
- Set.sInter_rangeproof · cited by 16
- DirSupClosedOn.sInterproof · cited by 4
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