Theorems · Theorem · order theory
lowerClosure_iUnion
∀ {α : Type u_1} {ι : Sort u_3} [inst : Preorder α] (f : ι → Set α), lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i)- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- LowerSetstatement · cited by 230
- lowerClosurestatement · cited by 83
- GaloisConnection.l_iSupproof · cited by 78
- gc_lowerClosure_coeproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- add_lowerClosureproof · cited by 2
- mul_lowerClosureproof · cited by 2
- lowerClosure_sUnionproof · cited by 0