Theorems · Theorem · order theory
DirSupClosed.union
∀ {α : Type u_1} {s t : Set α} [inst : Preorder α], DirSupClosed s → DirSupClosed t → DirSupClosed (s ∪ t)- Defined in
- Mathlib.Order.DirSupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
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
- DirSupClosedstatement and proof · cited by 31
- isLowerSet_univproof · cited by 8
- DirSupClosed.dirSupClosedOnproof · cited by 6
- DirSupClosedOn.unionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsClub.unionproof · cited by 0