Theorems · Theorem · order theory
lowerClosure_sUnion
∀ {α : Type u_1} [inst : Preorder α] (S : Set (Set α)), lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
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Cites9
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.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- Set.sUnionstatement · cited by 392
- LowerSetstatement · cited by 230
- lowerClosurestatement and proof · cited by 83
- Set.sUnion_eq_biUnionproof · cited by 51
- lowerClosure_iUnionproof · cited by 3
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